Question

A truck covers a certain distance at a certain speed. If speed is 4km/hr more than the original speed it would take 4 hr less to cover the same distance and if speed is 6 km/hr less than the original speed it would take 8 hr more than the normal time. Find the distance covered by the truck (in km)?

Answer 1

A truck covers a certain distance at a certain speed. If speed is 4km/hr more than the original speed it would take 4 hr less to cover the same distance and if speed is 6 km/hr less than the original speed it would take 8 hr more than the normal time. Find the distance covered by the truck (in km)?

Let:

The speed of the train be x km/hr, the time required for the journey be t hrs, and the distance be d km.

So, we have, in the first case, d = x * t …….(1)

In the second case, if the train is 10 km/hr faster, the speed would be (x+10) km/hr, and the time required would be (t-2) hrs. Thus we have, as the distance would be the same: d = (x+10)*(t-2)

Expanding, we have d = xt - 2x + 10t - 20. Substituting from equation (1), we get the simplified equation: 10t - 2x = 20 …….(2)

In the third case, if the train is 10 km/hr slower, the speed would be (x-10) km/hr, and the time required would be (t+3) hrs. Thus we have, as the distance would be the same: d = (x-10)*(t+3)

Expanding, we have d = xt + 3x - 10t - 30. Substituting from equation (1), we get the simplified equation: 10t - 3x = -30 …….(3)

Solving equations (2) and (3) simultaneously, we get x = 50 km/hr and t = 12 hrs.

Thus, distance d = x * t, that is d = 50 * 12 = 600km

Answer 2

Answer:

The distance is 41.142 km.

Explanation:

Let the actual speed of the train be x km/hr and the actual time taken be y hours. Then,

Distance covered $= xy$ km ..(1) [∴ Distance = Speed × Time]

If the speed is increased by 4 km/hr, then time of journey is reduced by 4 hours i.e., when speed is (x+4) km/hr, time of journey is (y−4) hours.

∴ Distance covered $= (x + 4)(y - 4)$

So,

$xy = (x - 4)(y - 4) \\ xy = xy - 4x - 4y + 16 \\ - 4x - 4y + 16 = 0 \\ 4x + 4y = 16 \\ x + y = 4......(2)$

When the speed is reduced by 6 km/hr, then the time of journey is increased by 8 hours i.e., when speed is (x−6) km/hr, time of journey is (y+8) hours.

∴ Distance covered =(x−6)(y+8)

So,

$xy = (x - 6)(y + 8) \\ xy = xy + 8x - 6y - 48 \\ 8x - 6y - 48 = 0 \\ 4x - 3y = 24.....(3)$

From equation (2),

$x + y = 4 \\ x = 4 - y.....(4)$

From equation (3) and (4),

$4(4 - y) - 3y = 24 \\ 16 - 4y - 3y = 24\\ 16 - 7y = 24 \\ - 7y = 24 - 16 \\ - 7y = 8 \\ y = - \frac{8}{ 7}$

From equation (3),

$x = 4 - ( - \frac{8}{7} ) \\ x = 4 + \frac{8}{7} \\ x = \frac{28 + 8}{7} \\ x = \frac{36}{7}$

Required distance is

$( - \frac{8}{7} ) \times ( \frac{36}{7} ) \\ = - \frac{288}{7} \\ = - 41.142 \: km$

Distance negative is not possible.

So negative sign is negligible.

We can say total distance is 41.142 km.

This is a problem of Speed and Distance chapter,

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