# Singapore 6A question help! X-post

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Here's the question:

Sam and Terry ran on the treadmill. Sam started 10 minutes before Terry. Terry finished 5 minutes before Sam. They both ran the same distance. When Terry finished, Sam had completed 4/5 of the journey and still had 1/2 mile to go.

Find Sam's speed.

Find Terry's speed.

I don't feel like we have enough information to do this, or if we do, it's hidden in some way I can't see. :blushing: Any help?

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Start here: "When Sam has completed 4/5 of his journey, he still has 1/2 mile to go."

How much time does it take Sam to complete that last 1/2 mile?

Then, knowing the time and distance for Sam's final stretch, can you figure out Sam's speed?

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I needed to draw a bar diagram.

Sam

|----------------------------------------------------------------------|

|---------------------------|-----------------------------|-------------|

Terry

If Sam finished 4/5 by the time Terry finished and ran for another 5 min, that means the last segment -- 1/5 -- took him 5 min. So the whole distance took 25 min. If he had 1/2 mile to go, the entire distance was 5*1/2 = 2 1/2 miles. So 2.5 miles/25 min, or 1/10 mile/min (do you need in in miles per min?)

If Sam started 10 min before Terry and finished 5 min after him, and Sam's total time was 25 min, then Terry's total time was 25-15=10 min. So 2.5 miles/10 min, or 1/4 mile/min.

Is that the right answer, lol?

(Sorry, I can't get my bar diagram to look right..)

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Sam ran for 15 minutes more than Terry. So, S = T + 15, where S and T refer to the time each boy spent running.

Both boys ran the same distance, which I will call d. Terry ran distance d in T minutes. Sam ran distance d in S minutes.

Speed = distance/time. I sill call Terry's speed t and Sam's speed s.

t = d/T and s = d/S That's too many variables to solve.

BUT we also know that when Sam had run for S-5 minutes, he had run 4d / 5 distance, and that distance was 0.5 miles less than d. So we have the equation

4d / 5 = d - 0.5 Let's solve for d

4d = 5d - 2.5

So d = 2.5 miles

Now let's plug 2.5 in for d --> t = 2.5/T and s = 2.5/S

We also remember that at S-5 minutes, Sam had run 2 miles. So we can also say that

s = 2/(S-5)

Therefore, 2 / (S-5) = 2.5 / S

By multiplying both sides by the denominators we get that

2S = 2.5 (S-5), or 2S = 2.5S - 12.5

0.5 S = 12.5, so S = 25 minutes

Plugging that into the equation, we get that

s = 2.5 / 25, or that s = 0.1 miles per minute

We know that S = T + 15, so therefore T = 10 minutes

t = 2.5/10, or 0.25 miles per minute

Hopefully I did that all correctly... I had a fussy baby and a rowdy 3yo screaming as I worked this out. ;)

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When using Singapore, your first step is to always use a bar graph like Kate demonstrated above. Fill in the information you have, and the solution starts to fall into place. I am such a visual learner, I know I learned more, teaching my kids with this program, than I did in College Calculus!

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