This is an SAT prep question. 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?
how do you draw a oblique discrete line
clearly the distance(D)each way is the same
so D/40 + D/30 + 1
solve for D
80
To find the total number of miles in the round trip, we can use the formula:
Distance = Speed × Time
Let's consider the time it took for the woman to drive to work at 40 miles per hour. If we let 'x' be the time taken in hours, we can write the equation:
40 * x = distance
Similarly, for the return trip at 30 miles per hour, we can write:
30 * (1 - x) = distance
Since the total traveling time was 1 hour, we can subtract 'x' from 1 to get the time traveled on the return trip.
Now we can solve these equations simultaneously to find the distance.
Rearranging the first equation, we have:
distance = 40 * x
Substituting this into the second equation, we get:
30 * (1 - x) = 40 * x
Solving for 'x':
30 - 30x = 40x
30 = 70x
x = 3/7
Now we can substitute this value of 'x' into our distance formula to find the total number of miles:
distance = 40 * (3/7)
distance = 120/7
Hence, the total number of miles in the round trip is 120/7 miles.