Question

5.On a120m track, a train travels the first 30km at a uniform speed of 30km/h. How fast must the train travel the next 90km so as to average 60km/h for the entire trip?

Answer 1

Answer:-

Let the speed for the next 90 km is "S".

Given:

Average speed = 60 km/h

Speed of the train for the first 30 km = 30 km/h

$Total \: time \: = 1 + \frac{90}{S} \\ \\ t = \frac{S + 90}{S} \: h$

Distance = 120 km

We know that,

$average \: speed \: = \frac{total \: distance \: travelled}{total \: time \: taken} \\ \\ 60 = \frac{120}{ \frac{S + 90}{S} } \\ \\ 60 = \frac{120 \times S}{S + 90} \\ \\ 60(S + 90) = 120S \\ \\ 60S + 5400 = 120S\\ \\ 5400 = 120S- 60S\\ \\ 60S = 5400 \\ \\ S = 90\:km/h$

Therefore, the train must travel at a speed of 90 km/h , so that the average speed is 60 km/h.