A boat takes 7 hours to travel downstream and 9 hours to travel upstream between two places on a river. If the speed of the stream is 2 km/h, what is the distance between the two places ?
126 km
Downstream speed = boat speed + stream speed and upstream speed = boat speed − stream speed, so the two speeds differ by twice the stream speed, here 2 × 2 = 4 km/h.
Step 1 — Let the distance be d km. Downstream speed = d/7 and upstream speed = d/9.
Step 2 — \(\frac{d}{7} - \frac{d}{9} = 4 \Rightarrow \frac{2d}{63} = 4 \Rightarrow d = 126\).
Step 3 — Check: downstream 126 ÷ 7 = 18 km/h, upstream 126 ÷ 9 = 14 km/h, boat 16 km/h and stream 2 km/h. 148 km, 120 km and 128 km do not give a stream speed of 2 km/h.
126 km option is correct.
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