Problem Solving

Source: Manhattan Prep

Car A started driving north from point X traveling at a constant rate of 40 miles per hour. One hour later, car B started driving north from point X at a constant rate of 30 miles per hour. Neither car changed direction of travel. If each car started with 8 gallons of fuel, which is consumed at a rate of 30 miles per gallon, how many miles apart were the two cars when car A ran out of fuel?

A. 30
B. 60
C. 90
D. 120
E. 150

The OA is C.

Given, total of 8 gallons fuel with 30 miles per gallon, total distance that can be covered is 8*30 = 240 miles.

Now, Car A travels with a rate of 40 miles per hr, so total time taken to cover 240 miles --> 240/40 = 6 hrs
Now to find total distance covered by Car B travelling at a rate of 30 miles per hr for the same time period(6 hrs as deduced from above) --> 30*6, however
since Car B started 1 hr after Car A, time period would be 6 - 1 = 5 hrs. Now, distance covered by Car B --> 30*5 = 150 miles

Hence Car B was 240 - 150 = 90 miles behind Car A when Car A ran out of fuel. $$$$