Distance for the whole race = 160 miles
Distance for first part = 90F miles
Distance for first part + Distance for last part = Distance for whole race
90F + Distance for last part = 160
Distance for last part = 160 - 90F
F represents the hours raced at the first part
L represents the hours raced at the first part
Time for whole race = 2 hours
Time for the first part + Time for the last part = Time for the whole race
F + L = 2.........................................(1)
Rate (mph) x Time (hours) = Distance (miles)
Time for the last part = (Distance for the last part) / Rate for the last part
L = (160-90F) / 60
60L = 160 - 90F
60L + 90F = 160...............................(2)
From equation (1)
F = 2 - L.............................(3)
Substitute equation (3) into equation (2)
60L + 90 (2 - L) = 160
60L + 180 - 90L = 160
90L - 60L = 180 - 160
30L = 20
L = 20/30
L = 0.67
Time for the last part = 0.67 hours
F = 2 - L
F = 2 - 0.67
F = 1.33
Time for the first part = 1.33 hours
Distance for first part = 90F
Distance for first part = 90(1.33)
Distance for first part = 119.7 miles
Distance for last part = 160 - 119.7
Distance for last part = 40.3
The complete table is shown below:
