A who travels 3 miles an hour, starts from a certain place five hours in advance of B who travels 4 miles an hour in the same direction. How many hours must B travel to overtake A?

Question

radar · Answer

When the distance traveled by A and B are equal then they have met and B then overtakes.  Use d=rt (distance = rate times time.

anonymous · Answer

3t = 4(t-5)

solve

radar · Answer

Note that 3t is distance of A and 4(t-5) is the distance of B.

anonymous · Answer

So how do I solve it?

radar · Answer

Are you an algebra student?

anonymous · Answer

yes, why? I know that distance = rate/time

radar · Answer

Use algebra and isolate t.  Use algebraic rules and get t on the left and its' value on the right:
t = ??

Hint clear the parenthesis of the equation provided by @sourwing

anonymous · Answer

3t = 4t-5

radar · Answer

and it is distance equals rate times time not divided by time.

radar · Answer

Now subtract 4t from both sides of the equal sign.  also correct your error when you cleared the parenthesis.

radar · Answer

You should of gotten 3t = 4t - 20

radar · Answer

3t - 4t = 4t -4t -20

radar · Answer

-t = -20  Now divide both sides by -1

anonymous · Answer

Where did you get 20 from?

anonymous · Answer

Never mind

anonymous · Answer

It will take 20 hours to overtake A.

radar · Answer

Final results t = 20 hours.  Should verify.
Verification    A distance 3 times 20 or 60 miles.
B distnace  4(20-5) = 60 miles       Yup, both traveled 60 miles.........good answer.

radar · Answer

Yes, cassieblake, 20 hours is good.  And good luck with your studies.

anonymous · Answer

Thanks, Do you think you can help me with another problem?

radar · Answer

I can try.

anonymous · Answer

Say the rise is 4 and the run is 2. If I were to increase both the rise and run by 1, would it be the same rate of change? Why or why not?

radar · Answer

No, the rate of change would not remain the same.  Here is why the original rise over run (rise/run) is 4/2 or 2.  Now if we add 1 to both the rise (getting5) and the run (getting 3) or rise over run is 5/3.  5/3 does not = 2 the resulting change is at a lower rate.

radar · Answer

You follow ??

anonymous · Answer

okay, thanks.

radar · Answer

You're welcome.