Theory question 102
Linear and Simultaneous EquationsA man left town M at 10:00 a.m. and travelled by car to town N at an average speed of 72 km/h. He spent 2 hours for a meeting and returned to town M by bus at an average speed of 40 km/h. If the distance covered by the bus was 2 km longer than that of the car and he arrived at town M at 1:55 p.m., calculate the distance from M to N.
Show the model answer
Model answer
Total time 10:00 to 1:55 = 3 h 55 min; travelling time = 1 h 55 min = 23/12 h
Let MN = x km: x/72 + (x + 2)/40 = 23/12
Multiply by 360: 5x + 9(x + 2) = 690 → 14x = 672
x = 48 km
Explanation
Take away the 2-hour meeting before setting up the time equation.