Question

It took Andrea 5.4 hours to drive to her mothers house on Sunday morning. On her return trip it took her 6 hours. Her average speed on Monday was 3 mph slower than on Sunday. What was her average speed on Monday?

Answer 1

The average speed on Monday is 27mph

Explanation:

Given

Let:

`1\to Sunday`

`2\to Monday`

So:

`t_1 = 5.4hr`

`t_2 = 6hr`

`s_2 = s_1 - 3` ---- average speed slower on Monday than Tuesday

Required

The average speed on Monday

Average speed is calculated as:

`Speed = (Distance)/(Time)`

`s = (d)/(t)`

Make d the subject

`d = st`

On Sunday, we have:

`d = s_1t_1`

`d = s_1 * 5.4`

On Monday, we have:

`d = s_2t_2`

`d = s_2 * 6`

The distance traveled is constant;

So:

`s_1 * 5.4 = s_2 * 6`

Make s1 the subject in:
`s_2 = s_1 - 3`

`s_1=3+s_2`

So, we have:

`(3 + s_2) * 5.4 = s_2 * 6`

Open bracket

`16.2 + 5.4s_2 = 6s_2`

Collect like terms

`6s_2 - 5.4s_2 = 16.2`

`0.6s_2 = 16.2`

Solve for s_2

`s_2 = 16.2/0.6`

`s_2 = 27`

The average speed on Monday is 27mph