Question

If a bicyclist is traveling at a speed of 10 km/h, he will be late by 1 hour. If he will travel at a speed of 15 km/h, then he will arrive an hour early. How fast should he travel to arrive on time?

Answer 1

The speed should he travel to arrive on time is 12 km/h

Explanation:

Given as :

Let the time taken by bicyclist = T h

If bicyclist travel with speed 10 km/h,

Then the time taken by him = ( T + 1 ) hours

Again

If bicyclist travel with speed 15 km/h ,

Then the time taken by him = ( T - 1 ) hours

Now Let The distance cover by bicyclist = D km = Speed × Time

So, As The distance cover is same for both case

∴ 10 × (T + 1 ) = 15 × (T - 1)

Or, 2 × (T + 1 ) = 3 × (T - 1)

Or, 2 T + 2 = 3 T - 3

Or, 3 +2 = 3 T - 2 T

∴ T = 5 hour

So, Distance cover by bicyclist = D = 10 × (5 + 1 )

Or, D = 60 km

So, new speed of bicyclist with time 5 hour and distance cover 60 km

New Speed =
`(Distance)/(Time)`

Or, New Speed =
`(60)/(5)`

∴ New Speed = 12 km/h

Hence The speed should he travel to arrive on time is 12 km/h Answer