3. The duration of a railway journey varies directly as the distance covered
and inversely as the velocity of the train. The velocity again varies
directly as the square root of the quantity of coal used per mile and
inversely as the number of carriages in the train. In a journey of 25
miles in half an hour with 18 carriages, 10 cwt. of coal is required.
Find how much coal will be required in a journey of 21 miles in
28 minutes with 16 carriages.
Answers
Given:
The duration of a railway journey varies proportionally to the distance.
The duration of a railway journey varies inversely as the velocity.
The velocity varies directly as the √coal used.
The velocity varies inversely as the number carriages.
Distance = 25 miles
Time = 30 min
Carriages = 18
Coal = 10 cwtt
To find:
The coal required for a journey of 21 miles in 28 minutes with 16 carriages.
Solution:
Calculate velocity for 25 miles,
Velocity = Distance / time
25/30
Original velocity = 5/6
Calculate velocity for 21 miles,
21/28
New velocity = 3/4
Hence, the amount of coal needed will be 9/16.
Calculate the amount of coal per mile for 25 miles train,
2/5 cwt of coal per
Substituting and solving using ratios,
2 / 5*coal required = 9/16
32 = 45 * coal required
Therefore,
Coal required = 0.71
Hence for 21 km,
We get,
21 * 0.71 = 14.91
Therefore, 14.91 cwt of coal will be consumed in a journey of 21 miles in 28 minutes with 16 carriages.