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Homework answers / question archive / Tom took 16 hours to drive the 1,000 highway miles from Chicago to Boston
Tom took 16 hours to drive the 1,000 highway miles from Chicago to Boston. He drove the first eight hours at constant speed, and then had to lower his speed considerably by 25 miles per hour for the remainder of his journey to Boston on account of construction. However, he maintained this constant lower speed for another 8 hours for the remainder of his journey to Boston. What was his lower speed.
When an object moves with constant speed V for a time interval t, the total distance D traveled by the object is:
D = V*t
Let Tom's initial speed be v miles per hour
The distance to traveled in the first t1 = 8 hours is:
d1 = v * t1 = 8v
Then his speed dropped by 25 mph, so now his speed is u=v-25
And the distance he traveled with this speed in t2 = 8 hours is:
d2 = u * t2 = (v-25)*8 = 8v-200
Together, the total distance Tom traveled is 1000 miles, therefore:
d1+d2 = 1000
8v + (8v-200) = 1000
16v -200 = 1000
16v = 1200
v = 1200/16 = 75mph
And in the second segment of his journey his speed was:
u = v-25 = 50 mph
