Question

On a drive from your home to town, you

wish to average 60 mph. The distance from
your home to town is 78 miles. However,
at 39 miles (half way), you find you have
averaged only 45 mph.
What average speed must you maintain in
the remaining distance in order to have an
overall average speed of 60 mph?
Answer in units of mph.

Answer 1

Your average speed must be 90 mph in the remaining distance in order to have overall average speed of 60 mph

Explanation:

The rule of distance is d = v × t, where

• v is the average speed

• t is the time

∵ You wish to average 60 mph on a drive from your home to town

∵ The distance from your home to town is 78 miles

→ Find the time of your journey using the rule above

∴ 78 = 60 × t

→ Divide both sides by 60

∴
`(78)/(60)` = t

∴ t =
`(13)/(10)` hours

∵ You have averaged only 45 mph in the first 39 miles (half way)

∴ v1 = 45 mph

∴ d1 = 39 miles

→ Find the time of this part

∴ 39 = 45 × t1

→ Divide both sides by 45

∴
`(39)/(45)` = t1

∴ t1 =
`(13)/(15)` hour

→ Subtract the time of the first part from the time of the journey to

find the time for the second part

∵ t2 = t - t1

∴ t2 =
`(13)/(10)` -
`(13)/(15)`

∴ t2 =
`(13)/(30)` hour

→ Now let us find the average speed of the second part of his journey

∵ d2 = 39 miles ⇒ (78 - 39)

∵ t2 =
`(13)/(30)` hour

∴ 39 = v2 ×
`(13)/(30)`

→ Divide both sides by
`(13)/(30)`

∴ 39 ÷
`(13)/(30)` = v2

∴ 90 = v2

∴ v2 = 90 mph

∴ Your average speed must be 90 mph in the remaining distance in

order to have overall average speed of 60 mph