Question

Your car gets 29 miles per gallon (mpg) at 60 miles per hour (mph) and 25 mpg a 70 mph. At what speed should you make a 525-mile trip:
If gas costs $3 per gallon and your time is worth $18 per hour
If gas costs $4 per gallon and your time is worth $12 per hour
If gas costs $5 per gallon and your time is worth $9 per hour

Answer 1

If gallon is giving me 29 miles per hour, for 525 miles, 525/29=18.1 gallons of gas is required and at 60 miles per hour for 525 mile I will need 525/60 = 8.75 Hours.

Similarly, If gallon is giving me 25 miles per hour, for 525 miles, 525/25=21 gallons of gas is required and at 70 miles per hour for 525 mile I will need 525/70 = 7.5 Hours.

If Gas Cost is $3 and Time is worth $18 per hour

At 60 mph speed:

Hence Cost of Gas = 3*18.1 = $54.3

Hence Cost of time = 18*8.75 = $157.5

Hence Total Cost = 54.3+157.5 = $211.8

At 70 mph speed:

Hence Cost of Gas = 3*21 = $63

Hence Cost of time = 18*7.5 = $135

Hence Total Cost = 63+135 = $198

Since cost is lower at 70 mph, Speed shall be 70 mph

If Gas Cost is $4 and Time is worth $12 per hour

At 60 mph speed:

Hence Cost of Gas = 4*18.1 = $72.4

Hence Cost of time = 12*8.75 = $105

Hence Total Cost = 72.4+105 = $177.4

At 70 mph speed:

Hence Cost of Gas = 4*21 = $84

Hence Cost of time = 12*7.5 = $90

Hence Total Cost = 84+90 = $174

Since cost is lower at 70 mph, Speed shall be 70 mph

If Gas Cost is $5 and Time is worth $9 per hour

At 60 mph speed:

Hence Cost of Gas = 5*18.1 = $90.5

Hence Cost of time = 9*8.75 = $78.75

Hence Total Cost = 90+78.75 = $168.75

At 70 mph speed:

Hence Cost of Gas = 5*21 = $105

Hence Cost of time = 9*7.5 = $67.5

Hence Total Cost = 105+67.5 = $172.5

Since cost is lower at 60 mph, Speed shall be 60 mph