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A car C1 left town A for town B. Another car C2 left town B for town A at the same time.
The ratio of the speeds of the 2 cars were 6:5 respectively.
After the stwo cars passed each other car A speed was reduced by 1/6 and car B was reduced by 1/4 .
When car A arrived at town B car B was still 54km from town A. What is the distance between A and B.
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Let d be this unknown distance between A and B, in kilometers.
The speed of the car C1 was initially 6x; the speed of the car C2 was initially 5x.
where x is some common measure of the speeds, in km/h.
The time from the start to the passing moment was 
= 
hours.
The distance traveled by car C1 from A to the passing point was time*speed = 
= 
hours.
The remaining distance for car C1 was 
kilometers.
The distance traveled by car C2 from B to the passing point was time*speed = 
= 
kilometers.
The speed of the car C1 after the passing moment was 
= 6x-x = 5x km/h.
The speed of the car C2 after the passing moment was 
= 
= 3.75x km/h.
To travel from the passing point to B, car's C1 travel time was 
= hours.
During this time, car C1 traveled the distance 
= km. (1)
During the same time, car C2 traveled the distance 
= 
km. (2)
The sum of distances (1), (2) and 54 km is exactly d
+ 
+ 54 = d. (3)
Multiply by 11 both sides of equation (3)
5d + 3.75d + 594 = 11d.
Simplify and find d
8.75d + 594 = 11d
594 = 11d - 8.75d
594 = 2.25d
d = 594/2.25 = 264.
ANSWER. The distance from A to B is 264 kilometers.
Solved.
