solve the following word problem

Question

On the main street, the tourists walked for s km with a speed of v km/hour. On the side road, the tourists walked twice the distance that they covered on the main street. How much time t (in hours) did the tourists spend if it is known that on the side road they walked with a speed that was 2 km/hour less than their speed on the main road? Find t when s=10, v=6.

On the main street, the tourists walked for s km with a speed of v km/hour. On the side road, the tourists walked twice the distance that they covered on the main street. How much time t (in hours) did the tourists spend if it is known that on the side road they walked with a speed that was 2 km/hour less than their speed on the main road? Find t when s=10, v=6.

Answer 1

You can make use of the formula: distance = rate x time

 

On the main street, the tourists walked a distance of s km at a rate of v km/h. The time t is unknown, so we can call it t₁

 

Plugging into the above formula gives us:

 

s = vt₁

 

On the side road, the tourists walked a distance of 2s km (twice the distance walked on the main street), at a rate of (v - 2) km/h, which is 2 km/h less than the rate on the main street. Since the problem does not state that the amount of time walked on the main street and the side road is the same, then we will call the time walked on the side road t_2. Using this info, we again plug into the formula to obtain:

 

2s = (v - 2)t₂

 

You can now substitute the given values of s and v to solve for t₁ and t_2.