A woman drove to work at an average speed of 40 miles per hour and returned along the same route at 30 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?

went t hours at 40

went (1-t) at 30
so
40 t = 30 (1-t)
70 t = 30
t = 3/7 of an hour
distance at 40 = (3/7)(40) = 120/7
distance at 30 = (4/7)(30) = 120/7 better be the same:) check
so total distance = 240/7

Her average speed was 35 miles per hour. Since the round trip took her 1 hour, what was the total number of miles in the round trip?

If you post your answer, we'll be glad to check it.

I forgot to mention that this is an SAT question of the Day and they give you options for answers. The options are:

30
30 1/7
34 2/7
35
40
Sorry if the way I put it was confusing.

240/7 = 34 2/7

not allowed to use average because distance, not time, is the same

I did not see that SAT question of the day. I usually do them.

Oh, this question is from a while ago. They are very helpful in preparing for the SAT. Thank you for your help.

To determine the total number of miles in the round trip, we need to calculate the distance traveled in one direction and then double it.

Let's start by finding the distance traveled in the first leg of the trip, where the woman drove to work at an average speed of 40 miles per hour. We can use the formula:

Distance = Speed × Time

Let's denote the distance traveled in the first leg as D1.

So, D1 = 40 miles/hour × t1

Next, let's find the distance traveled in the return leg, where the woman drove back at 30 miles per hour. Since she covered the same route, the distance in the return leg will also be D1.

Therefore, D2 = 30 miles/hour × t2

Given that the total traveling time was 1 hour, we can express the relationship between the two time periods:

t1 + t2 = 1 hour

Now, let's substitute the values of D1 and D2 into the equation:

40 miles/hour × t1 + 30 miles/hour × t2 = D1 + D2

Since D1 = D2, we can simplify the equation as:

40t1 + 30t2 = 2D1

Substituting t2 = 1 - t1, we get:

40t1 + 30(1 - t1) = 2D1

Expanding the equation:

40t1 + 30 - 30t1 = 2D1

Combining like terms:

10t1 + 30 = 2D1

Simplifying:

10t1 = 2D1 - 30

Dividing by 10:

t1 = (2D1 - 30)/10

We know that t1 + t2 = 1, so we can substitute t1 in the equation:

(2D1 - 30)/10 + t2 = 1

Multiplying by 10 to eliminate the fraction:

2D1 - 30 + 10t2 = 10

Rearranging the equation:

2D1 + 10t2 = 40

Since D2 = D1, we can substitute D2 with D1:

2D1 + 10t2 = 40

Again, since D1 = D2, we have:

2D1 + 10t2 = 40

Let's substitute t2 = 1 - t1:

2D1 + 10(1 - t1) = 40

Expanding the equation:

2D1 + 10 - 10t1 = 40

Combining like terms:

2D1 - 10t1 = 30

Rearranging the equation:

10t1 = 2D1 - 30

Dividing by 10:

t1 = (2D1 - 30)/10

Now we have a system of two equations:

t1 = (2D1 - 30)/10

t2 = 1 - t1

We can solve this system of equations to find the values of t1 and t2.

By substituting t1 = (2D1 - 30)/10 in t2 = 1 - t1, we get:

t2 = 1 - (2D1 - 30)/10

Simplifying:

t2 = (10 - 2D1 + 30)/10

t2 = (40 - 2D1)/10

t2 = (20 - D1)/5

Since the total traveling time is 1 hour, we have:

t1 + t2 = 1

(2D1 - 30)/10 + (20 - D1)/5 = 1

Expanding the equation:

(2D1 - 30 + 2(20 - D1))/10 = 1

(2D1 - 30 + 40 - 2D1)/10 = 1

Simplifying:

10/10 = 1

The equation is satisfied. This means that our initial assumption that D1 = D2 is correct.

So, the distance of the round trip is given by:

Total distance = 2D1 = 2 × Distance of the first leg

Therefore, the total number of miles in the round trip is 2D1. You can find the value of D1 by substituting the value of t1 into the equation D1 = 40t1.