Question 59

A travelled a total distance of 3990 km. He travelled part of the distance by air, part by water and the rest by land. The time he spent on them was in the ratio 1 : 16 : 2 respectively. The average speed of each mode of travel was in the ratio 20 : 1 : 3 respectively. If A’s overall average speed was 42 km/h, the distance covered by air is

Solution

Assume the time spent on each commutation mode is t, 16t, and 2t.

Similarly, the average speed of each of the commutation modes is 20s, s, and 3s.

Now, the distance travelled on each of the commutation modes is 20st, 16st, and 6st. The sum is 42st, which shall be equal to 3990 km.

Hence, st= $$\frac{3990}{42}$$, which is 95.

We are given that the overall average speed is 42 kmph. Average speed is the ratio of total distance (3990 km) and total time (19t).

So, 42= $$\frac{3990}{19t}$$, which means t= 5. Hence, from the value of 'st' (95), we can say that s=19.

The distance by air is 20st, which is 20$$\times$$19$$\times$$5, which is 1900 km.