b) Two points A and B on a highway are 70 km apart. An autorickshaw starts from A
and another autorickshaw starts from B simultaneously. If they travel in the same
direction, they meet in 7 hours. However, if they travel towards each other, they
meet in 1 hour. Find the speed of the two autorickshaws.
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When they travel in same direction, suppose
they meet when B travels for x m, then A will have travelled 70+x
m in the same time
Since, Speed =TimeDistance
Speed of car at A =7x+70
And Speed of car at B =7x
And when they travel in the opposite direction, suppose they meet when A
travels for y m, then B will have travelled 70−y m in the same
time
Speed of car at A =1y=y
And Speed of car at B =170−y=70−y
Equating the speeds of the cars in both the cases,
Speed of car at A, 7x+70=y
x+70=7y
=>x−7y=−70 --- (1)
Speed of car at B, 7x=70−y
=>x+7y=490 --- (2)
Adding equations 1 and 2, we get 2x=420=>x=210
So, Speed of car at A =7x+70=7280=40km/hr
Speed of car at B =7x=7210=30km/hr
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