Question

The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey ?

Answer 1

We have the following data to find the speed for the second part of the journey:
Total distance to be travelled by train (D) = 200 km
Average speed required (v_avg) = 70 km/hr
Time required for the entire journey (T) :
`"Time" = "Total Distance"/"Average speed"`
= `200/70` hr

T = `20/7` hr
For the first part of the trip:
Distance covered (d₁) = 100 km
Speed for this part of journey (v₁) = 50 km/hr
Time taken for the first part of journey :
`"Time" = "Distance travelled"/"Speed"`
So,
t₁ = `100/50` hr
= 2 hr
For the second part of the trip,
Distance covered (d₂) = 100 km
Time taken for the second part of journey :
t₂ = T-t₁ 

= `(20/7 - 2)` hr
= `6/7` hr
Speed of the train for the second part of the journey : 

= `"distance travelled"/"Time"`
= `((100)(7))/6`
= 116.67 km/hr