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| Math Central | Quandaries & Queries |
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Question from Dilshad, a parent: Chuong and Hassan both drive 40 km from home to work each day. One day Chuong said to Hasssan, "If you drive home at your usual speed, I will average 40 kmph faster than you and arrive home in 20 minutes less time." Find Hassan's speed. |
Hi Dilshad,
The important fact here is that distance equals time times rate. Suppose that Hassan drives at $v$ kmph and it takes him $t$ hours to travel the 40 km. Then $40 = t \times v.$
His claim is that if he increases his speed to $v + 40$ kmph his time to travel the 40 km will be 20 minutes less. 20 min is $\frac13$ of an hour so at this increased speed he will travel the 40 km in $t - \frac13$ hours. Again using the fact that distance equals time times rate we get
\[40 = (t - \frac13) \times (v + 40).\]
Expand the right side and use the fact that $40 = t \times v$ to eliminate $v$ from the above equation and solve for $t.$ Finally use $40 = t \times v$ again to find $v.$
Penny
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