math problem help

Question

Jalen is training to run the mini-marathon. Today during his run he went at a rate of 3.5 mph for 20 minutes to warm up, then sped up to 5.25 mph. The whole workout took an hour and a half. How far did he go?

 

Answer 1

Lanai, the first thing to do is give names to the unknown quantities.

The problem asks for total distance in miles.

Let d be the total distance

Are there other unknowns?

It helps to know the equation for time and distance problems:

distance = rate * time

Now write down equations that translate the other information.

First leg of the training run:

distance1 = 3.5 * 20/60 (divide the time by 60 minutes per hour)

distance2 = 5.25 * ?/60

So here was the other unknown, the amount of time spent at the higher speed.

Let t = time spent at higher speed

what else do we know about t?

We know that the total spent was an hour and a half. That means total time = 1.5

So t = 1.5 - 20/60 = 1.5 - .3 = 1.2

now let’s put that into the second equation

distance2 = 5.25 * 1.2

and remind ourselves of the first equation

distance1 = 3.5 * .3

since d = 5.25 * 1.2 + 3.5 * .3

just do the arithmetic.