if the ratio of speed of A to B is 5:4, then what start can A give to B so that in a 1km race B must cover 10% less distance than A?
Answers
Given : ratio of speeds of a and b is 5:4,
To find : what start can a give to b so that in a 1km race, b must cover 10% less distance than a
Solution:
Speed of A = 5S km/hr
Speed of B = 4S km/hr
A will cover 1 km
b must cover 10% less distance than a => 1 - (10/100)1 = 0.9 km
Let say x km (0 < x < 1) is the start given to B
Minimum Distance remained for B = 0.9 - x km
Time taken by B = (0.9 - x)/4S hr
Time taken by A = 1/5S hr
1/5S = (0.9 - x)/4S
=> 4 = 4.5 - 5x
=> 5x = 0.5
=>x = 0.1 km
=> x = 100 m
At least 100 m start to be given to b
He will cover 100 m + 800 m = 900m
while a will cover 1000m ( 1 km)
0.1 km = 100 m start to be given so that b must cover 10% less distance than a
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Answer:
Distance covered by B in 6 sec = ( 1000/300 ×6)=20 m
Therefore, A beats B by 20 m.
For a dead-heat race, A must give B a start of 20 m.