Question

a car made a 60 mile trip at an average speed of 20 mph. On the return trip, the car's average speed was 30 mph. What was the average speed of the car car for the entire two-way trip?​

Answer 1

Speed = 24 mph

Explanation:

Distance traveled in the two way trip

2*(60 miles) = 120 miles

Time it took to arrive to the destination (first travel, 60 miles, 20mph)

Speed = distance/ time

t = distance/ speed = (60 miles) / (20 mph) = 3 hours

Time it took to come back (return travel, 60 miles, 30 mph)

t = (60 miles) / (30 mph) = 2 hours

Total time = (3 +2) hours = 5 hours

So the average speed is

Speed = (120 miles) / (5 hours) = 24 mph

Answer 2

The average speed of the car is
`s = 24\ mph`

Explanation:

The average speed is defined as

`s = (d_1)/(t)`

Where

s is the speed

d is the displacement made

t is the time it took to perform the displacement d.

On the first trip the speed was 20 mph and the displacement was 60 miles. Then we find the time
`t_1`

`s = (d)/(t)`

`t_1 = (d_1)/(s)\\\\t_1 = (60)/(20)\\\\t_1 = 3\ h`

On the second trip the speed was 30 mph and the distance traveled was the same: 60mph

We calculate
`t_2`.

`t_2 = (60)/(30)\\\\t_2 = 2\ h`.

Now we can calculate the average speed for the entire route

`s = (d_1 + d_2)/(t_1 + t_2)\\\\s = 60 +(60)/(3) +2\\\\s = (120)/(4)\\\\s = 24\ mph`