Solving Esther's Morning Commute Problem

[maria vega]

Homework Statement

Esther drove to work in the morning at an average speed of 40 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work how many miles did Esther drive to work in the morning?

Homework Equations

The Attempt at a Solution

40(time she took in the morning, or p) = x
30(time she took in the evening, or q) = x

Therefore 40(p) = 30(q), or divide both sides by 5 and get 8(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.

Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.

Therefore 8(60-q) = 6q or 480-9q = 6q. So 480 = 14q, which makes q = 34.2857 If q = 34.2857, then by (p+q)=60, p (the time she took in the morning) must equal 25.714285.
Then (25.714285/60) x 40 = 23.80 miles I think

Am I correct?

 

[cepheid]

Therefore 40(p) = 30(q), or divide both sides by 5 and get 8(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.

It's not worth the fraction of a second it takes to divide by 2 and get 4p = 3q?

Therefore 8(60-q) = 6q or 480-9q = 6q.

Where did the 9 come from?

EDIT: Just realized you canceled out that mistake with another one by saying that the sum of the q terms was 14q (the correct answer) even though what you wrote would have yielded 15q as a result.

EDIT 2: Although your numerical answers for p and q seem correct, your final answer for the distance is not correct.

 

[maria vega]

ok Therefore 40(p) = 30(q), or divide both sides by 5 and get 8(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.

Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.

Therefore 8(60-q) = 6q or 480-8q = 6q. So 480 = 14q, which makes q = 34.2857 If q = 34.2857, then by (p+q)=60, 30 x (34.825/60) = 17.1425 is this it? the distance of his house to the office

 

[cepheid]

ok Therefore 40(p) = 30(q), or divide both sides by 5 and get 8(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.

LOL. This doesn't make any more sense than it did the first time you wrote it. They're both even numbers. It takes almost no time for the extra step of dividing them by 2.

Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.

Therefore 8(60-q) = 6q or 480-8q = 6q. So 480 = 14q, which makes q = 34.2857 If q = 34.2857, then by (p+q)=60, 30 x (34.825/60) = 17.1425 is this it? the distance of his house to the office

Yeah, that answer seems about right.

 

[maria vega]

thank youuu!