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

Answer:

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

Step-by-step 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

Answer 2

Answer:

225 miles

Step-by-step 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

$\frac{distance}{time} =$ hours

For return trip time taken = $\frac{x}{45}$

The difference in time is 1 hour

$\frac{x}{45}-\frac{x}{50}=1\\\frac{10x-9x}{450} =1\\x=450$

Hence answer is 450 miles

Verify:

Going time=$\frac{450}{50} =9$ hrs

Return time = $\frac{450}{45} =10$ hrs

i.e. 1 hour more verified