Distance word problem?

Question

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

Please explain how to do this

Answer 1

You just need the formula, D = ST, twice.
The distance is the same each way.
Let T = time to drive to work.
The total time is 1 hour, so time to drive home is (1 - T) hours.
Driving to work, we have : D = 45T
Driving to home, we have : D = 30(1 - T)
Both D's are equal, so 45T = 30(1 - T).
Therefore, T = 2/5 hours.
Distance to work is thus : 45 * 2/5 = 18 miles.
And you get the same distance by calculating 30(1 - 2/5).

Answer 2

Esther drove 1.5 or 3/2 times as fast in the morning as in the afternoon, so it took her the reciprocal of 3/2, or 2/3 as much time in the morning as in the afternoon to make the trip. If we call her time in the afternoon t, then her time in the morning is (2/3)*t

2/3*t + t = 1 hour (her total travel time, morning and afternoon)
5/3*t = 1 hour (combining 2/3*t with t, which can also be written 3/3*t)
t = 1/(5/3) hours = 1 * 3/5 hours = 3/5 hours

Driving 3/5 hours at 30 mph would take her 3/5 * 30 miles, or 18 miles. Since she took the same route both directions, Esther drove 18 miles to work.

Answer 3

18 miles

the ratio of 45:30 in terms of minutes in 1 hour is 36:24

in 24 minutes she drove (at 45mph as its the faster spoeed hence shorter time) 18 miles

check: at 30 mph it wlll take 36 minutes to drive 18 miles

so it is correct - she spent 24 minutes driving 18 miles in the morning and 36 minutes driving 18 miles in the evening - total 1 hour driving time to and from work

Answer 4

23

Answer 5

37.5 miles...... based on 37.5 mph. The average of 45 m/hr and 30 m/hr