# Speed, Distance and Time

The following questions are again taken from “Mathematical Brain-Teasers” by J.A.H Hunter. You will need to be familiar with the relationship between speed, distance and time and be able to solve simultaneous equations.

Again the second question is more challenging than the first, although both are difficult. The wording of the second question is confusing, so make sure you read it carefully. Good Luck!

1. Joan looked at her watch as the car pulled in to pick her up. “Right on time” she told her husband as she opened the door. “I bet you speeded.” He shook his head and said “No, I just started at the right time. If I’d averaged 6mph faster I’d have been five minutes early, but at 5mph slower and I’d have been 6 minutes late.” How far had he driven?
2. If Sam had driven for 20mins less than the time he would have driven if he had driven 20 miles less than he did drive but at two-thirds the speed at which he drove, he would have driven 10 miles less than he did. If he had driven for 20mins longer than the time he would have driven if he had driven 10 miles less than he did drive but at three-quarters the speed at which he drove, he would have driven 20 miles further than he did. Confused? How far did Sam drive?