Question

Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?

(need shown work for review)

Answer 1

Hello.

Let's call the initial speed 'x'. When driving at that speed, Jeremy's father takes 20 minutes to arrive to the school. When driving 18 mph faster (x + 18), he gets there in 12 minutes. Therefore:

20 - x
12 - x + 18

As they're inversely proportional:

12 - x
20 - x + 18


`(12)/(20) = (x)/(x+18)`

`12x + 216 = 20x`

`216 = 8x`

`x = (216)/(8)`

`x = 27`

That means that the initial speed is of 27mph. Since we have the time and the speed, we can find the distance:

Average Speed = Total Distance Travelled / Time Interval

20 minutes = 0.33h


`27 = (Distance)/(0.33)`

`Distance = 27.0.33`

`Distance = 12.21 miles`

Hope I helped and good luck.

Answer 2

9

Explanation:

Let's make the speed of the dad's driving in rush hour x miles per minute. (I'm just doing miles per minute because it uses minutes.)

Then, when there's no traffic, it's x miles per minute+18 miles per hour=x miles per minute+0.3 miles per minute(18/60).

So basically, we've got this:

x miles per minute=20min

x+0.3 miles per minute=12min

Now, using the formula, d(distance)=t(time)*s(speed), I'm going to find x.

d=20x=12(x+0.3)=12x+3.6

As you can see here, 8x=3.6. Therefore, x=0.45. Now, back to the formula. d=20x. Since you know what x is, this is easy. d=9