Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

Almighty:

anonymus:

[quote=\"Dharma\"]
Hi dharma,

Very many thanks for yr continuous support...I'm still confused...As anonmus said
Its the diameter of THAT (shaded portion's )semicircle also..right.I understand yr first explanation ie., Perimeter of the shaded part
= Length of the 3 sides of a triangle + Curved length of the semicircle..but y can't i think like this???I treat the shaded portion as a seperate semi circle with its diameter 14 cm. Not the diameter of the big circle...
Anonmus..if u are clear with Dharma's explanation.please clarify to me toooooo...

[/quote]Hi Almighty,

The side of the triangle (14cm) which touches the circle at 2 points and gives us one the shaded portion is NOT the diameter of the semicircle. The individual shaded portions are not separate and the question also does not suggest that. There is only 1 circle in this question.

The 3 curved lengths/arc are NOT semi-circles individually BUT together they form a semi circle.

Hope it is clearer now.

[Almighty]

Dharma:

Almighty:

[quote=\"anonymus\"]

[/quote]
Thankyou very much Dharma..I now know why i should not think so. So grateful of u to be so patient in replying..

[Dharma]

Almighty:

Dharma:

[quote=\"Almighty\"]

[/quote]
No prob.

[Herbie]

I have one speed qn which need help.


A lorry travelled at an average speed of 72km/h from Pink Town to Happy Town. 50 minutes later, a van started out from the same point towards the same destination at an average speed of 90km/h, reaching Happy Town at the same time.

a. How long did the van take to travel from Pink Town to Happy Town?
b. If both the lorry and the van arrived at Happy Town at 4.05pm at what time did the lorry start out??

Tx.

[MOE Hater]

Herbie:

I have one speed qn which need help.


A lorry travelled at an average speed of 72km/h from Pink Town to Happy Town. 50 minutes later, a van started out from the same point towards the same destination at an average speed of 90km/h, reaching Happy Town at the same time.

a. How long did the van take to travel from Pink Town to Happy Town?
b. If both the lorry and the van arrived at Happy Town at 4.05pm at what time did the lorry start out??

Tx.

I think that an important point to note is that the time taken by the van to overtake the lorry is the same as the time taken by the van to reach Happy Town

Original Distance between 2 vehicles = 72 km/h x 5/6 h
= 60 km

Difference in speeds = 90 km/h - 72 km/h
= 18 km/h

Time van took to overtake lorry = Time van took to reach Happy Town
= 60 km / 18 km/h
= 3 1/3 h

Time lorry took to reach Happy Town = 3 1/3 h + 5/6 h
= 4 1/6 h

Time van started off -> 4 1/6 h before 4.05pm -> 11.55am

Hope this helps

[singmathstutor]

Herbie:

I have one speed qn which need help.


A lorry travelled at an average speed of 72km/h from Pink Town to Happy Town. 50 minutes later, a van started out from the same point towards the same destination at an average speed of 90km/h, reaching Happy Town at the same time.

a. How long did the van take to travel from Pink Town to Happy Town?
b. If both the lorry and the van arrived at Happy Town at 4.05pm at what time did the lorry start out??

Tx.

1. Calculate how much the lorry has travelled when the van first starts to move.

Lorry
Speed = 72km/h
Time = 50min = 5/6h
Distance = 72km/h x 5/6h
= 60km

2. Determine the difference in speed between the 2 vehicles

Lorry = 72km/h
Van = 90km/h
Difference = 90km/h-72km/h
= 18km/h

3. Determine the time for the van to catch up on the lorry

Time taken for van to catch up on lorry = Time taken for van to complete its journey from Pink Town to Happy Town

The lorry was 60km ahead of the van when the van started its journey, and for every 1h, the van would have make up ground on the lorry by 18km,

Time = 60km/18km/h
= 3 1/3h (Ans for a)

4. Determine time taken for lorry to complete its journey

Time = 3 1/3h + 5/6h
= 4 1/6h

5. Determine time lorry starts its journey

Use timeline and deduct 4 1/6h from 4.05pm
Time started = 11.55am (Ans for b)

[Almighty]

Please clarify on the below speed problem.

Edmund drove Andrew from Jurong Point to Woodlands at a constant speed of 75 Km/h. Andrew rested for 20 mins before walking 3km home at a speed of 6km/h.Edmund took 15 minutes to return to Jurong Point to pick Ben up. HE then drove to Orchard at 75Km/h.The three people reached their destinations at the same time. What was the distance Edmund drove from Jurong Point to Orchard?
My method:
Time taken by Andrew to walk home from
Jurong point to Orchard = 65mins
6km ---- 1hr
3 km ----- ( 3/6 ) = 30min
30 + 20+ 15 = 65min

Speed of Edmund is 75km/hr
60 min ---- 75Km
65 min ----(65X75/60) = 81.25Km
Distance Edmund drove from Jurong Point to Orchard = 81.25 km (MY Answer)

Book Ansswer:
Total time taken by Andrew to reach home = 20+ 30 = 50 min (WHat happened to 15 mins?)
Time taken by Edmund to drive from jurog to Orchards = 50 -15 = 35 min
= 7/12h
Distance covered = 75 * 7/12 = 43.75km
Cannot understand marked in red.
Can anyone clarify??? :?

[singmathstutor]

We should be looking at the question in perspective from the time Andrew alighted at Woodlands.


In Andrew’s case, to reach his destination (home) after alighting at Woodlands,
Total time he needs is 20min for resting and
30min for walking home at a speed of 6km/h in a distance of 3km.
T= 3km/6km/h
=1/2h
=30min

Therefore, the 20min+30min=50min is as such.

In Ben and Edmund’s case, we should start comparing the time just when Edmund has started his return trip to JP to pick Ben. Since 15min is used to make that trip, and both the boys would have reached Orchard at the same as Andrew reaching home, therefore time left for their journey to Orchard is 50min-15min=35min

That 15min is only applicable to Ben and Edmund’s journey, so you should not have added 15min to Andrew’s return trip.

Hope this would have helped to clear your doubts

[Dharma]

Herbie:

I have one speed qn which need help.


A lorry travelled at an average speed of 72km/h from Pink Town to Happy Town. 50 minutes later, a van started out from the same point towards the same destination at an average speed of 90km/h, reaching Happy Town at the same time.

a. How long did the van take to travel from Pink Town to Happy Town?
b. If both the lorry and the van arrived at Happy Town at 4.05pm at what time did the lorry start out??

Tx.

For constant distance;
Speed ratio=> Lorry : Van = 4 : 5
Time ratio => Lorry : Van = 5 : 4
5u – 4u = 1u = 5/6hrs

a)\tTime taken by van = 4u = 4 x 5/6 hrs = 3 1/3hrs
b)\tTime taken by lorry = 5u = 25/6hrs = 4 1/6hrs
Time lorry left Happy Town => 4 1/6 hrs before 4.05pm = 11.55am

[Herbie]

Thanks Dharma.


I have another speed qn.

Town S and Town T are 600km apart.
At 9am, a van travelling at an uniform spped left Town S for Town T
At the same time, a car set off from Town T to Town S at an uniform speed which was 12km/h faster than the van’s

Find the average speed of the car if the two vehicles met at 3pm.

TX