Lance is a local scrap merchant. He had to travel to the county recycling plant, 60 miles away. On the way there he could only manage a steady 12 miles per hour (mph), fully laden.
On the way back,Lance could manage a steady 16mph. He placed 24 gallons of fuel in the tank ready for the round trip, thinking that this would be enough as the wagon managed to travel 8 miles per gallon.
Unfortunately, a piece of metal pierced his fuel pipe at the start of the trip and the wagon started to lose 1 gallon of fuel per hour.
Luckily he only lost fuel when moving and he lost no fuel whilst unloading his scrap metal.
Were 24 gallons enough for the round trip?
g(t) is amount of gas in tank at time t, t in hours
Speed in miles per hour, part one: 8, part two: 12
Miles / gallon of gas is 8 MPG for both parts.
Trip 1 takes 5 hours, 60 miles / 12 mph
Trip 2 takes 60/16 = 15/4 hours
part one of the trip
g(0) = 24
g(t) = 24 - t - 12*t/8
g(t) = 24 - 2.5t
g(5) = 11.5
part two of the trip when (t > 5)
g(t) = g(5) - (t-5) - 16*(t-5)/8
g(t) = 16.5 - t - 16*(t-5)/8
g(t) = 26.5 - 3t (valid for t>5)
t (end of the trip) = 5 + 60/16 = 8.75
g(8.75) = 26.5 - 3*8.75 = 26.5 - 26.25
Yes, there will be .25 gallons of fuel remaining
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Posted by Larry
on 2023-08-06 08:48:32 |
p&p math
