desaichinmay22 wrote:
Two cars start moving simultaneously in different directions from point A at constant respective uniform speeds . What is the difference between their speeds (faster minus slower)?
(1) After 2 hours, the two cars are 140 miles apart
(2) When the faster car has covered a distance of 200 miles, the slower car has covered 150 miles
Yes, different directions doesn't necessarily imply opposite direction. They could move away from each other at any angle.
Statement 1 only tells you the distance between them. It doesn't tell us the distance covered by them together. If they moved in opposite directions, 140 would be the distance covered by them. If they moved perpendicular to each other, together they would have covered distance more than 140.
Statement 2 only tells us that the ratio of their speed is 200:150 = 4:3. We don't know what their actual speeds are.
Using both, we don't know the distance traveled by them together so we don't know their individual speeds. We cannot find the difference between their speeds. e.g.
Say they travel opposite to each other, their combined speed is 140/2 = 70 miles/hr. So their independent speeds are 40 miles/hr and 30 miles/hr. Difference in their speeds = 40 - 30 = 10 miles/hr
Say they travel perpendicular to each other, the distance between them is the hypotenuse of the right triangle and is 140. The distance traveled by them will be in the ratio 4:3 (legs of the triangle) so the 140 represents the side 5. Multiplier is 140/5 = 28. So the legs of the triangle are 4*28 and 3*28. Their speeds then are 4*28/2 = 56 miles/hr and 3*28/2 = 42 miles/hr. Difference between their speeds is 56 - 42 = 14 miles/hr
Answer (E)
+1. Thank you for the explanation.