The distance from home to school at a speed of 6 km / h can be walked 1 minute faster

The distance from home to school at a speed of 6 km / h can be walked 1 minute faster than at a speed of 5 km / h to find this distance

Let’s translate the value of speeds and time in SI:

v1 = 6 km / h = 1.7 m / s;

v2 = 5 km / h = 1.4 m / s;

t = 1 minute = 60 seconds.

Let S be the distance from home to school. Then, in the first case, with a speed v1 = 1.7 m / s, it is equal to:

S = v1 * t1

In the second case, with a speed v2 = 1.4 m / s, it is equal to:

S = v2 * t2

It is known from the problem statement that t2 = t1 + 60. Then:

v1 * t1 = v2 * (t1 + 60)

v1 * t1 = v2 * t1 + 60 * v2

v1 * t1 + v2 * t1 = 60 * v2

t1 * (v1 – v2) = 60 * v2

t1 = 60 * v2 / (v1 – v2) = 60 * 1.4 / (1.7 – 1.4) = 60 * 1.4 / 0.3 = 280 seconds.

S = v1 * t1 = 1.7 * 280 = 476 meters.

Answer: the path to the house to the school is 476 meters.