On a certain trip, Edgar drives 231 km in exactly the same time as Erwin drives 308 km. If Erwin's rate exceeded that of Edgar by 13 kph. Determine the rate of Erwin.

**Distance = rate x time**

distance

----------- = time {from formula, multiplied each side by rate}

rate

231

----- = Edgar's time {substituted Edgar's information}

r

308

-------- = Erwin's time {substituted Erwin's information, Erwin's rate exceeded Edgar's by 13 kph}

r + 13

231/r = 308/(r + 13) {their times were equal}

231r + 3003 = 308r {cross-multiplied in the proportion}

3003 = 77r {subtracted 231r from each side}

r = 39 {divided each side by 77}

r + 13 = 52 {substituted 39, in for r, into r + 13}

**Erwin's rate was 52 kph**

*- Algebra House*