A train covered half of the distance between stations A and B at the speed of 48 km/hr, but then it had to stop for 15 min. To make up for the delay, it increased its speed by 53 m/sec and it arrived to station B on time. Find the distance between the two stations and the speed of the train after the stop.
Choose the correct answer
A) 206
B) 216
C) 226
D) 256
E) 246

Rationale: first let us determine the speed of the train after the stop . the speed was increased by 53 m / sec = 5 ⋅ 60 ⋅ 6031000 km / hr = 6 km / hr . therefore , the new speed is 48 + 6 = 54 km / hr . if it took x hours to cover the first half of the distance , then it took x − 1560 = x − 0.25 hr to cover the second part . so the equation is : 48 ⋅ x = 54 ⋅ ( x − 0.25 ) 48 ⋅ x = 54 ⋅ x − 54 ⋅ 0.25 48 ⋅ x − 54 ⋅ x = − 13.5 − 6 x = − 13.5 x = 2.25 h . the whole distance is 2 × 48 × 2.25 = 216 km . answer is b .
Answer: B