Multiple choice

Priya and Neeraj can row a boat at 12 km/h and 16 km/h, respectively, in still water. In a river flowing with a constant velocity, Neeraj takes 1 hour more to row 30 km upstream than to row the same distance downstream. If Priya starts from a certain point in the river, rows downstream to some location, and then immediately returns upstream to the same starting point, taking a total of 90 minutes, what is the total distance, in km, that Priya will cover?

  1. 4

  2. 8

  3. 12

  4. 16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let river speed be v. Neeraj: 30/(16-v) - 30/(16+v) = 1. Solving gives v=4. Priya: 12 km/h, downstream speed 16, upstream 8. Time = d/16 + d/8 = 1.5 hours. 3d/16 = 1.5, d = 8. Total distance = 2d = 16.

AI explanation

Using Neeraj's speed of 16 km/h, the equation for his 30 km upstream and downstream trips is 30 divided by (16 - v) minus 30 divided by (16 + v) equals 1, where v is the stream's speed. Solving gives v equal to 4 km/h, making Priya's downstream speed 16 km/h and upstream speed 8 km/h. Let the one-way distance be d; the total time equation is d divided by 16 plus d divided by 8 equals 1.5 hours. Multiplying by 16 gives d plus 2d equals 24, so d equals 8 km, making the total distance 8 plus 8, which is 16 km.

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