I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?

gnistory Jun 27, 2024

#1**0 **

*I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?*

When you go faster you'll get there sooner, so the problem

must actually mean "would have arrived 45 minutes **earlier**."

Distance = Rate • Time

There are two cases: (1) D = (40)(t)

(2) D = (50)(t – 45 / 60)

Regarding 45 / 60 - Since the speed is given in miles per hour, the 45 minutes

must be converted to hours to keep units consistent. We could have converted

the speed to miles per minute, but that would have unnecessarily added tedium.

Since the distance is the same in both cases, set them equal and solve for time.

(50)(t – 45 / 60) = (40)(t)

50t – 37**.**5 = 40t

10t = 37**.**5

t = 3**.**75

Substitute t back into case (1) D = (40)(3**.**75)

**D = 150**

__check answer__

Substitute t back into case (2) D = (50)(3**.**75 – 0**.**75)

D = (50(3**.**00)

D = 150

_{.}

Bosco Jun 27, 2024