A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find the distance the car has covered.
Pick:
A) 114
B) 115
C) 116
D) 117
E) 118

Rationale: the driver did not plan the stop at c . suppose it took x hours for him to get from c to b . then the distance is s = 40 ⋅ x km . it took x − 3060 − 1560 = x − 4560 = x − 34 h to drive from c to b . the distance from c to b is 32 ( x − 34 ) km , which is 28 km shorter than 40 ⋅ x , i . e . 32 ( x − 34 ) + 28 = 40 x 32 x − 24 + 28 = 40 x 4 = 8 x x = 12 hr ⋅ x = 30 min . then the time of the trip from c to b was 30 min . the distance covered equals 3 ⋅ 32 + 12 ⋅ 40 = 96 + 20 = 116 km . so answer is c .
Answer: C