Question 177527
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.
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