Answer:
35 miles
Step-by-step explanation:
Let's say Fritz travels at x miles per hour via train and y miles per hour via car.
(speed of car) + 80 miles per hour = speed of train
y + 80 = x
Speed * time = distance
Speed of train * time of train = distance = speed of car * time of car
x * 15 minutes = y * 35 minutes
convert minutes to hours since miles per hour is in terms of hours
60 minutes = 1 hour
15 minutes = ? hours
multiply 15 minutes by 1 hour/60 minutes. since 60 minutes = 1 hour, we can divide both sides by 60 minutes to get 1 hour/60 minutes = 1. we can always multiply by 1, so we do that here. note that the minutes are in the denominator so the 15 minutes cross out with the 60 minutes, leaving us with only hours as our unit.
15 minutes = 15 minutes * 1 = 15 minutes * 1 hour/60 minutes = 15/60 hours = 3/12 hours
similarly, 35 minutes * 1 hour/60 minutes = 35/60 hours = 7/12 hours
x * 15 minutes = y * 35 minutes
x * 3/12 hours = y * 7/12 hours
plug y+80 in for x
(y+80) * 3/12 hours = y * 7/12 hours
(3/12) * y + 20 = (7/12) * y
subtract (3/12) * y from both sides to isolate the variable (y) and its coefficient
20 = (4/12) * y
multiply both sides by 12/4 (the inverse of the coefficient) to get rid of the coefficient
20*12/4 = y = 60
y = 60 miles per hour
x = y + 80 = 140 miles per hour
distance = x * 3/12 hours = 140 miles/hour * 3/12 hours= 35 miles
