average speed

[gayu]

A certain car average 25 miles/gallon of gasoline when driven in city and 40 miles/gallon when driven on highway. According to these rates, which of the following is closest to no. of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on highway?
A)28 B)30 C)33 D)36 E)38

[manpsingh87]

A certain car average 25 miles/gallon of gasoline when driven in city and 40 miles/gallon when driven on highway. According to these rates, which of the following is closest to no. of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on highway?
A)28 B)30 C)33 D)36 E)38

Miles per gallon that car averages= total distance/ total time;

total distance = 50+10=60;
total time =t1+t2; here t1 is the time taken while traveling 10 miles at the speed of 25 miles/ gallon and t2 is the time taken while traveling 50 miles at the speed of 40 miles per gallon;
t1=10/25=2/5;
t2=50/40=5/4;
total time= 2/5+5/4=8+25/20=33/20;

therefore miles per gallon that averages= 60/(33/20)= 1200/33 ~36 hence D

[vkb001]

@manpsingh87 Though your answer is correct, the average miles per gallon is not total-distance/total-time. It should be total-miles/total-gallons-used.

Total miles = 10 + 60 --(1)
Total gallons = 10/25 + 50/40 = 2/5 + 5/4 --(2)

Average miles per gallon = (1)/(2) ~ 36 (D)

[manpsingh87]

@manpsingh87 Though your answer is correct, the average miles per gallon is not total-distance/total-time. It should be total-miles/total-gallons-used.

Total miles = 10 + 60 --(1)
Total gallons = 10/25 + 50/40 = 2/5 + 5/4 --(2)

Average miles per gallon = (1)/(2) ~ 36 (D)

try to visualize the problem... its a simple average speed concept.. but trick here is instead of giving speed in m/h its been mentioned in miles/gallons... why i write total time used is to make clear,,, that underlying concept should be the same.. no matter.. what language an examiner used.. we must be able to visualize it..!!!! total miles and total distance both means the same thing.. miles is a unit for measuring distance, length in fact it could be meter, kilometer... so it doesn't matter.. whether we write miles or distance....!!!

i hope it clears your doubt..!!!!