Inequality Maths

Question

A train needs 4 hours to go from the first station to the second. If the third station is 120 miles away and the total travel time must be no more than 7 hours, write an inequality that would let you find the slowest average speed, v, the train could have

Answer 1

4 hours from station A to station B

C is 120 miles away and total travel time < 7 hours

average slowest speed the train could have is?

IF A to C = 120 miles

and A to C takes 7 hours or less

then average speed can't be less than 120/7 = 17 1/7 mph

v = 17 1/7 mph = slowest speed to get to C in 7 hours

17 1/7 mph times 7 hours = 120 miles

UNLESS It's not 120 miles from A to C, but 120 miles from B to C

then 7 hours total is from 120 miles + distance from A to B

and time from B to C = 7-4 = 3 hours

120/3 = 40 mph = v = average speed

odds are you want 40 mph

as it seems more realistic

and it uses the information of 4 hours from A to B

which distance would be 4x40 = 160 miles

280 total miles in 7 hours

280/7 = 40 mph

v > 40mph

in order to do the full trip in no more than 7 hours