SAT math question?

Question

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

pls list out the steps!

Thanks for your help!!

Answer 1

Speed = Distance/Time

Lets assume the following:

Distance to work = D
Time taken in the morning T1.
Time taken in the evening T2

So, we can change S=D/T (speed = distnace/time) to look like T=D/S

In the morning, Equation 1:
T1 = D/45

In the evening, Equation 2:

T2 = D/30 (she drive the dame distance)

Add Equation 1 and 2.

T1 + T2 = D/45 + D/30

We know that T1 + T2 = 1 hour.

Therefore

1= D/45 + D/30

which can be written as

1 = (2D+3D)/90

which can be written as 90 = 5D

Or the Distance is 18 Miles.

Hope this helps.

Answer 2

If the distance is d miles,
time taken to drive to work = d/45 hr and
time taken to return home = d/30
As the total time is 1 hr,
d/45 + d/30 = 1
=> d = 1 / (1/45 + 1/30)
= [(45) * (30)] / (45 + 30)
= 18 miles

Answer 3

Decide on a naming convention:
Let's use variables subscripted "1" for the trip to work, and variables subscripted "2" for the trip back from work.

List your knowns and unknowns:
Given:
v1 = 45 mi/hr
v2 = 30 mi/hr
d1 = d2 (because she took the same route)
t1 + t2 = 1 hr (total commute time)
Required:
d1 (the distance to work in the morning)

Then list out equations you think would be relevant for this problem. How bout this one:
d = vt (the distance-avg speed-time relation)

Solution:
Manipulate the relevant equation with the knowns, so that you get a set of two equations in 't1' and 't2'. Solve that system, substitute your answer for t1 to get d1, and you have your answer.

Answer 4

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Answer 5

distance/rate = time
let x be the distance

x/45 + x/30 = 1
multiply all terms by 90

2x + 3x = 90
5x = 90
x = 18 miles

Answer 6

x = distance to work
x/45 +x/30 = 1hour
2x +3x = 90 [Multiply both sides by 90]
5x= 90
x = 18 miles