Bret started on a 70mile bicycle ride at 20milesper hour Aft

Bret started on a 70mile bicycle ride at 20milesper hour. After a time he became a little tired and slowed down to 12miles per hour for the rest of the trip. The entire trip of 70 miles took 4.5 hours. How far had bret ridden when he reduced his speed to 12 miles per hour?

Solution

let x = amount of time bret rode at 20 miles per hour.
let y = amount of time bret rode at 12 miles per hour.
rate times time = distance
distance = 70
20*x + 12*y = 70
total time was 4.5 hours
x + y = 4.5
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from x + y = 4.5 we can derive x = (4.5 - y)
substitute in the equation:
20*x + 12*y = 70 to get:
20 * (4.5 - y) + 12 * y = 70
simplify to get:
20 * 4.5 - 20 * y + 12 * y = 70
90 - 8*y = 70
add 8*y to both sides and subtract 70 from both sides to get:
20 = 8*y
divide both side by 8 to get:
y = 20/8 = 2.5
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x + y = 4.5
x + 2.5 = 4.5
x = 2.0
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you have:
x = 2.0
y = 2.5
substitute in the original equation of:
20*x + 12*y = 70
to get:
20*(2.0) + 12*(2.5) = 70
40 + 30 = 70
70 = 70
values are good.
2.0 + 2.5 = 4.5
values are still good.
x = 2.0
y = 2.5
x = amount of time bret rode at 20 miles per hour
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your answer is:
bret rode 20 miles per hour for 2 hours when he reduced his speed to 12 miles per hour.