Learning Resources

For this problem recall the relationship between distance, rate and time. If the distance and rate are used we express the time as .

Let n represent the rate at regular speed to finish the trip

and (n - 20) represent the rate at the reduced speed to finish the trip

Then the time at the regular rate will be and the time at the reduced rate will be . Since the reduce rate is 1 hour longer we have as an equation to represent the problem. Solve as follows:

From this quadratic equation we have a = 1, b = -20 and c = -4800. Substitute into the quadratic formula and solve.

From this solution we see that n = 80  or n = -60 which is an inadmissible root since speed cannot be negative.

Since 80 km/h is the usual speed then 60 km/h will be the slower speed.