math problem help! You don't have to give me the answer, just explain me how to do it.?

Question

Esther drove to work in the morning at an average speed of 45 mph. She returned home in the evening along the same route and averaged 30 mph. If esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?

I appreciate your help.

Answer 1

Call the distance you need d. In that case, the time she spent traveling in the morning is:

d/(45 mph)

The time she spent traveling in the evening is:

d/(30 mph)

The total time must equal 1 hour:

d/(45 mph) + d/(30 mph) = 1 hour

Solve for d:

d = (1 hour)/( 1/(45 mph) + 1/(30 mph) )

And you get:

d = (1 hour)/( 1/(18 mph) )

and thus:

d = 18 miles

I hope that helps.

Answer 2

Define the number of miles driven in the morning as x. (I'll assume she also drives the same x back home as well).

If you think about it, 45mph is a ratio. In the morning, she drives 45 miles for every hour on the road. You can turn this around and say for every mile Esther drives,. she's been driving 1/45th of an hour. 1/45 hours per mile times x miles would then be the number of hours Esther drives in the morning.

Similarly, on the way home, she drives 1/30 hours per mile. and 1/30x would be her time driving home. We can add those two times together and set them equal to 1 hour.

--- 1/45 (x) + 1/30 (x) = 1

Solving this equation for x would then get your distance...

--- 1/45 (x) + 1/30 (x) = 1
--- 2/90 (x) + 3/90 (x) = 1
--- 5/90 (x) = 1
--- x = 90/5 = 18 miles

Answer 3

Do 45 and 30 make you think of 90, a nice simple multiple of both of them? Let's see what happens if it's 90 miles to work. Yes, we know it isn't, but it will make it easy at first, and we can fix it later.

90 miles at 45 mph would take 2 hours in the morning, and the same 90 miles at 30 mph would take 3 hours in the evening, making five hours. But it's not five hours, we are told it's actually one hour. So we were out by five times. Make it a fifth of 90 miles and it must come to 1 hour.

Answer 4

First of all you need to realize the main term connecting the two. The main thing in this is time: 1hr and the mph's (miles per hour<--time again) she drove.

From the statement here's what you know:

morning drive was 45mph
evening drive was 30mph
The addition of the two trips were 1 hr. (SAYS ABOVE)

45 or 30 miles per hour are 45miles/60min or 30miles/60min

so if x (the number of miles) is multiplied by 45/60 and 30/60 you get this equation:

x(45/60) + x(30/60) = 60

you can easily solve for x =)
Just reduce, distribute and do all those other goofy things.
need help? I'm not far!!

Answer 5

It took her 60/45 minutes to drive each mile in the morning, and 60/30 minutes to drive each mile home. Let M be the mileage each way. Then M(60/45) + M(60/30) = 60 (the total commute time). Solve for M and you're done.

Answer 6

let's say from home to work is x miles.
since it took total of one hour for a round trip,

x/45+x/30=1
(2x/90)+(3x/90)=1
5x/90=1

x=....