Question

In a 1000 metres race, manish gives ravi a headstart of 40 metres and beats him by 19 seconds. if manish gives ravi a headstart of 30 seconds, then ravi beats manish by 40 metres. find the ratio of manish's speed to ravi's speed.

Answer 1

x = speed of manish

y = speed of ravi

total distance = 1000 m

Case 1 :  manish gives ravi a headstart of 40 metres and beats him by 19 seconds

d₁ = distance travelled by manish = 1000 m

d₂ = distance travelled by ravi = 1000 - 40 = 960 m

t₁ = time taken by manish to travel = d₁ /x = 1000/x

t₂ = time taken by ravi to travel = d₂ /y = 960/y

given that : t₁ = t₂ + 19

(1000/x) = (960/y) + 19

1000/x = (960 + 19y)/y

x = 1000y/(960 + 19y)                                      eq-1

Case 2 :  manish gives ravi a headstart of 30 seconds, then ravi beats manish by 40 metres

d₁ = distance travelled by manish = 960 m

d₂ = distance travelled by ravi = 1000  m

t₁ = time taken by manish to travel = d₁ /x = 960/x

t₂ = time taken by ravi to travel = d₂ /y = 1000/y

given that : t₂ = t₁ + 30

(1000/y) = (960/x) + 30

using eq-1

(1000/y) = (960/(1000y/(960 + 19y) )) + 30

(1000/y) = (960(960 + 19y)/(1000y)) + 30

y = 1.63 m/s

using eq-1

x = 1000(1.63)/(960 + 19(1.63))  

x = 1.64 m/s

ratio = x/y = 1.64/1.63 = 1.01

Answer 2

Step-by-step explanation:

equating times taken individually in both cases, we get answer of 6:5