PLEASE HELP QUICK MATH QUESTION

Question

anonymous · Answer

I am helping my friend move by driving his car cross country behind the rental truck he is driving. As we start, he points out that the car needs gasoline. He says he’ll go on ahead because the truck will go only 55 mph and I can catch up with him. That was at 8 a.m. After filling the tank I leave the gas station 15 minutes behind him. If I drive 60 mph, how long will I have to drive for AND how many miles will I have driven to catch up with him?

jhannybean · Answer

$$t_2 = 15 + t_1$$

jhannybean · Answer

So his rate, $r_1 = 55 ~mph$, $r_2 = 60~mph$ I believe.

anonymous · Answer

@Jhannybean so how would u solve for it?

zepdrix · Answer

$$\Large\rm distance=rate\cdot time$$

$$\Large\rm d=55\cdot \left(t+\frac{1}{4}\right)$$(This guy left 15 minutes earlier, so he traveled for t and 15 minutes. I wrote 1/4 because we're thinking of t in terms of hours. So he traveled a quarter of an hour longer).

$$\Large\rm d=60\cdot t$$

They traveled the same distance whenever they met up,$$\Large\rm 55\left(t+\frac{1}{4}\right)=d=60t$$$$\Large\rm 55\left(t+\frac{1}{4}\right)=60t$$
Solve for t to figure out how much time passed before they met up.
Plug that t value into either equation to figure out the distance at which they met up.

zepdrix · Answer

t being in hours is important for the equations because their rates are given in (miles per HOUR).