Sumati traveled from point A to point B at 475 m/min. The moment that Sumati reached point B, Rachna set off from point B, at a speed 1.6 times the speed at which Sumati traveled and reached point C. If the total distance covered from A to C via B was 45.6 km and the time taken from when Sumati started from point A to when Rachna reached point C was 75 minutes, what is the distance between A and B?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 19 km.
Speed of Sumati = 475 m/min
Speed of Sumati in km/hr = 475 × 0.06 = 28.5 km/hr
Speed of Rachna = 1.6 × 28.5 = 45.6 km/h
Total distance from point A to point C = 45.6 km
Let's assume the distance between A to B = x
B to C = 45.6 - x
Time taken to travel from points A to C = 75 min or 75/60 = 1.25 hours
⇒ x/28.5 + (45.6 - x)/45.6 = 1.25
⇒ 45.6x + 1299.6 - 28.5x = 1624.5
⇒ 17.1x = 324.9
⇒ x = 324.9/17.1
⇒ x = 19 km