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# The race

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I always forget formulas!!! This question has a formula:

Sarah and Jack are in a running race. Jack ran at 6 mph. Sarah ran at 4 mph. Jack finished the race 1 hour before Sarah. How long was the race?

What is the formula to that question?

Pyramid  Oct 2, 2014

#1
+85759
+18

We have.......

Rate*Time = Distance  ......  so let Jack's time be "T' ....and we have 6T = D

And since Sarah ran 1 hour more, we have...... R(T + 1) = D  →  4(T + 1) = D

And since the distances are the same, we have

6T = 4(T + 1)     ....simplify

6T = 4T + 4    ...... subtract 4T from both sides

2T = 4    ....... divide by 2 on both sides

T = 2 hrs = Jack's time  ...  and  Sarah's time was 1 hour more = 3 hrs.

So, the race was 6mph*(2hrs) = 4mph*(2 + 1)hrs = 4mph(3 hrs) = 12 miles  !!!

CPhill  Oct 2, 2014
Sort:

#1
+85759
+18

We have.......

Rate*Time = Distance  ......  so let Jack's time be "T' ....and we have 6T = D

And since Sarah ran 1 hour more, we have...... R(T + 1) = D  →  4(T + 1) = D

And since the distances are the same, we have

6T = 4(T + 1)     ....simplify

6T = 4T + 4    ...... subtract 4T from both sides

2T = 4    ....... divide by 2 on both sides

T = 2 hrs = Jack's time  ...  and  Sarah's time was 1 hour more = 3 hrs.

So, the race was 6mph*(2hrs) = 4mph*(2 + 1)hrs = 4mph(3 hrs) = 12 miles  !!!

CPhill  Oct 2, 2014
#2
+271
+5

Pyramid  Nov 18, 2014

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