Question

23. A tour bus averaged 50 miles per hours

between two cities on the first leg of
a trip and 45 miles per hour on the
return trip. The return trip took
hour longer. Find the distance between
the two cities.​

Answer 1

225 miles

Explanation:

Given that a tour bus averaged 50 miles per hours between two cities on the first leg of a trip and 45 miles per hour on the return trip.

Let the distance be x. Then we get time taken for to trip would be

`(distance)/(time) =` hours

For return trip time taken =
`(x)/(45)`

The difference in time is 1 hour

`(x)/(45)-(x)/(50)=1\\(10x-9x)/(450) =1\\x=450`

Hence answer is 450 miles

Verify:

Going time=
`(450)/(50) =9` hrs

Return time =
`(450)/(45) =10` hrs

i.e. 1 hour more verified

Answer 2

The distance between the cities is 50*4.5 = 225 miles.

Explanation:

Let "t" be the time spent on the first leg at the average speed of 50 miles per hour.

Then (t+0.5) is the time spent on the returning trip at the average speed of 45 miles per hour.

Since the distance is the same in both directions, you have an equation

50*t = 45*(t+0.5).

Simplify and solve it for "t".

50t = 45t + 22.5,

5t = 22.5

Divide both sides by 5

t = 22.5/5

= 4.5.

Thus we found the time spent at the speed 50 mph. It is 4.5 hours.

Thus the distance between the cities is 50*4.5 = 225 miles