   SEARCH HOME Math Central Quandaries & Queries  Question from Michael, a student: If Tina swims 4 miles upstream at 1 mph and back downstream to the same point to the same point at 4 mph, what is her average speed? Hi Michael,

Tina's average speed is her total distance divided by the total time. It doesn't seem there is enough information here because you can't find the distance she swims or the time it takes, but let's try anyway.

Let the distance she travels upstream be d miles and the time it takes her to swim this distance be t hours. Since upstream she swims at 1 mph

d/t = 1

and hence

d = t

(That looks strange since the units of d are miles and the units of t are hours, but it just means that the numbers d and t are the same.)

Downstream she travels the same distance but at 4 mph. How long does it take her?

What is the total distance she travelled?
What is the total time it took?
What is her average speed?

Penny

Michael wrote back

Hi!
I sent the following question in yesterday, and though I was happy with the speedy response, I found the
the question without answering with a definite answer... I'm more confused now than I was with the question!

When I did the test, here were the multiple choice answers:

A. .8 mph
B. 1.6 mph
C. 2.5 mph
D. 3 mph

Out of those answer, which is the most correct?

Thanks so much for helping me out, you guys do great
work...
Michael

Michael,

My intention was not to do the question for you but to break it down into steps so that you could complete it yourself. I started by letting d be the distance she travells upstream and t be the time it takes for this part of the trip. I then observed that since she travells 1 mph going upstream the numbers d and t are the same. Furthermore I know that going downstream the distance she travells is also d miles. Then I asked

Downstream she travels the same distance but at 4 mph. How long does it take her?

Downstream she travells at 4 time the speed as going upstream so It will take her 1/4 the time. Hence the time to travel
d miles downstream is 1/4 t hours.

Now can you answer the remaining three questions?

What is the total distance she travelled?
What is the total time it took?
What is her average speed?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.