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# Speed questions--help!

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Mr Tan was travelling from Town L to Town M at a uniform speed.He drove past Mr Samy who was travelling at a uniform speed of 76 km/h in the opposite direction.1.5 hours later,Mr Tan reached Town M while Mr Samy was still 26 km away from Town L.Mr Tan took 4 hours to travel from Town L to Town M.Find the distance between the two towns.

May 23, 2017

#1
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Mr Tan was travelling from Town L to Town M at a uniform speed.He drove past Mr Samy who was travelling at a uniform speed of 76 km/h in the opposite direction.1.5 hours later,Mr Tan reached Town M while Mr Samy was still 26 km away from Town L.Mr Tan took 4 hours to travel from Town L to Town M.Find the distance between the two towns.

Let X be the point where they pass each other

That is 1.5 hours into Mr Tan's trip, he has another 2.5 hours to travel.

In that in 2.5 hours My Sammy travels  76*2.5 = 190km which which is 26km less than LX.

So    LX=26+190 = 216km

Mr Tran took 1.5 hours to travel this 216km  so he is travelling at  216/1.5 = 144km/hour

(He is one speedy gonzales!)

After thay pass Mr Tran travels another 2.5 hours       144*2.5=360km    So XM=360km

therefore

LM = 216+360 = 576km

May 23, 2017
#2
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Average speed = Distance / Time
NOTE: After the two men meet, Mr. Tan drives for another 1.5 hours.
Let the distance between the 2 towns = D
Let the average speed of Mr. Tan = S. But we have:
4S = D. And we also have Mr. Sammy driving:
1.5*76 + 26 =140 km - The distance Mr. Tan had to cover in 1.5 hours. Therefore, Mr. Tan's average speed:
140/1.5 =93 1/3 Km/h. And the distance between the 2 towns:
D =4 hours x 93 1/3 Km/h = 393 1/3 Km.

May 23, 2017
#3
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Mr Tan was travelling from Town L to Town M at a uniform speed.He drove past Mr Samy who was travelling at a uniform speed of 76 km/h in the opposite direction.1.5 hours later,Mr Tan reached Town M while Mr Samy was still 26 km away from Town L.Mr Tan took 4 hours to travel from Town L to Town M.Find the distance between the two towns.

Call Mr. Tan's rate, R

The total distance between the  towns  = Mr. Tan's Rate * 4 hrs = 4R....and this equals to

The distance that  Mr. Tan traveled in (1.5) hrs  =   1.5R    plus

The distance that Mr Sammy traveled  in 1.5 hrs  + 26 km  =   1.5(76)  + 26 km

So we have this

4R  =  1.5R  +  1.5 (76)  +  26  simplify

2.5R  =  140    divide both sides by  2.5

R  = 56 km / hr  =   Mr. Tan's Rate

So.....the total distance between the towns  =  4 * (56)  =  224 km   May 23, 2017
#4
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CPhill's answer is the CORRECT one:

Distance =1.5S(Mr. Tan's leg) + (1.5*76 +26)(Mr. Sammy's leg) =4S and S =56 Km/h x 4 =224 Km.

May 23, 2017