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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.

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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