SOLUTION: Mary can jog, on average, 2 miles per hour faster than her husband, James. James can jog 6.6 miles in the same amount of time it takes Mary to jog 9 miles. Mary can jog _________

Click here to see ALL problems on Square-cubic-other-roots

Question 942488: Mary can jog, on average, 2 miles per hour faster than her husband, James. James can jog 6.6 miles in the same amount of time it takes Mary to jog 9 miles. Mary can jog __________ miles per hour?
Another word problem I can not comprehend
Found 4 solutions by macston, MathTherapy, josgarithmetic, greenestamps:
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website!
M=Mary's rate J=Jame's rate
M=J+2 Mary is 2mph faster than James
6.6 mi/J=9 mi/M James runs 6.6 miles in the time it takes Mary to run 9 miles
Substitute M=J+2 in the second equation to solve for J
6.6/J=9/J+2 Multiply each side by J
6.6J/J=9J/J+2
6.6=9J/J+2 Multiply each side by J+2
6.6(J+2)=9J(J+2)/(J+2)
6.6J+13.2=9J subtract 6.6J from each side
6.6J+13.2-6.6J=9J-6.6J
13.2=2.4J Divide each side by 2.4
13.2/2.4=2.4J/2.4
5.5=J So James can run at 5.5 mph and Mary runs at 7.5 mph (J+2)
CHECK
James runs 6.6 miles in 6.6 mi/5.5 mph=1.2 hrs
Mary runs 9 miles in 9mi/7.5 mph=1.2 hrs

Answer by MathTherapy(10898)   (Show Source):
You can put this solution on YOUR website!

Mary can jog, on average, 2 miles per hour faster than her husband, James. James can jog 6.6 miles in the same amount of time it takes Mary to jog 9 miles. Mary can jog __________ miles per hour? Another word problem I can not comprehend ************************************ This is a typical TRAVEL problem, with the typical DST (Distance = Speed x Time) formula, or Let Mary's speed, be S Since she jogs 2-mph faster than James, James' speed = S - 2 Time Mary takes to jog 9 miles: ; Time James takes to jog 6.6 miles: Since the time Mary takes to jog 9 miles is the same that James takes to jog 6.6 miles, then we get the following TIME equation: 9(S - 2) = 6.6S ----- Cross-multiplying 9S - 18 = 6.6S 9S - 6.6S = 18 2.4S = 18 Mary's jogging-speed, or

Answer by josgarithmetic(39851)   (Show Source):
You can put this solution on YOUR website!

SPEED TIME DISTANCE MARY j+2 t 9 JAMES j t 6.6

Those two time quantites same variable given as equal so

--

MARY can jog at miles per hour.

Answer by greenestamps(13392)   (Show Source):
You can put this solution on YOUR website!

The responses from the other two tutors use the same basic approach, although the setup from the two tutors is different. Their basic approach is this:

"The times are the same, so write and solve an equation that says the times for the two runners are equal"

Time is distance divided by speed, so the equation looks like this:

Mary's distance husband's distance -------------------- = -------------------- Mary's speed husband's speed

In this problem, the equation might then be

A different approach that I usually prefer (because it "works" for me!) is this:

"The times are the same, so the ratio of distances is the same as the ratio of speeds"

For this problem, then, the equation is
Mary's distance Mary's speed -------------------- = ------------------ husband's distance husband's speed

With this approach, the equation for this problem will be

Algebraically, the two starting equations are equivalent, and cross multiplying in either equation leads to exactly the same place. So one approach is not any better than the other.

So this is one example of where a student should consider different methods for solving a problem and find the one that "works" best for him.

SOLUTION: Mary can jog, on average, 2 miles per hour faster than her husband, James. James can jog 6.6 miles in the same amount of time it takes Mary to jog 9 miles. Mary can jog __________