Two bicyclists cover the same path by cycling at the rate of 9 and 10 km/hr respectively. Find the length of journey of one takes 32 minutes longer than other.
Answers
Given data : Two bicyclists cover the same path by cycling at the rate of 9 and 10 km/hr respectively.
To Find : The length of journey of one takes 32 minutes longer than other.
solution : according to given data, both cyclists cover the equal distance.
Let, speed of cyclists A be 9 km/hr and speed of cyclists B be 10 km/hr and assume that cyclist A take 32 minutes more time than cyclist B.
We know,
⟹ 32 minute = 8/15 hour
Now,
⟹ speed of B = distance/time
⟹ 10 = distance/time
⟹ 10 = distance/x
⟹ distance = 10x ----{1}
Let, time taken by A to cover distance be x
similarly,
⟹ speed of A = distance/time
⟹ 9 = distance/time
⟹ 9 = distance/(x + 8/15) {according to given data}
⟹ distance = 9 (x + 8/15) ----{2}
Now, from eq. {1} and eq. {2}
⟹ 10x = 9 (x + 8/15)
⟹ 10x = 9x + 72/15
⟹ 10x - 9x = 72/15
⟹ x = 72/15
⟹ x = 24/5
⟹ x = 4.8 hour
Put value of x in eq. {1}
⟹ distance = 10x
⟹ distance = 10 * 4.8
⟹ distance = 48 km
Answer = The length of the journey is 48 km
{Verification : put distance = 48 km in eq. {2}
⟹ distance = 9 (x + 8/15)
⟹ 48 = 9 (x + 8/15)
⟹ 48/9 = x + 8/15
⟹ 16/3 = x + 8/15
⟹ x = 16/3 - 8/15
⟹ x = 80/15 - 8/15
⟹ x = 72/15
⟹ x = 24/5
⟹ x = 4.8
Hence it verified.}
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