SOLUTION: A bus travels from Town A to town B at constant speed. It passes a car travelling at constant speed of 90km/h from the opposite direction. 1 1/2 hours later the bus reaches town B

Question 99321: A bus travels from Town A to town B at constant speed. It passes a car travelling at constant speed of 90km/h from the opposite direction. 1 1/2 hours later the bus reaches town B but the car is only 25km away from town A. If the bus took 4 hours to complete the whole journey,What is the distance between the 2 towns?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bus travels from Town A to town B at constant speed. It passes a car traveling at constant speed of 90km/h from the opposite direction. 1 1/2 hours later the bus reaches town B, but the car is only 25km away from town A. If the bus took 4 hours to complete the whole journey,What is the distance between the 2 towns?
:
Let d = distance between the two towns AB:
:
Speed of the car = 90
:
Speed of the bus = d/4; (speed = dist/time)
:
Trying to visualize this will help:
A-------25------------x--------------B
:
They met at x
:
Bus was at x, 1.5 hrs from B, or 2.5 hr from A (Total time given as 4 hrs)
:
When bus reaches B,
Car = 90*1.5 = 135 km from x
:
It tells us the car is 25 km for A at this time
Therefore:
x = 135 + 25 = 160 km from A
:
Find the speed of the bus:
2.5 hrs to reach x, which is 160 km from A
Bus speed = 160/2.5 = 64 km/hr
:
We know that the speed of the bus also = d/4
d/4 = 64
d = 64 * 4
d = 256 km is the distance between the two towns
:
:
Check solution by seeing if the car took 1.5 hr to travel the 135 km from x
to a point 25 km from A
:
Speed = 135/1.5 = 90 km/hr which is the speed given for the car
:
There may be a simpler, more elegant, way to do this, but it escapes me.

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