A rower travels upstream at 6km/h and back to the starting place at 10km/h. The total journey takes 48 minutes. How far upstream did the rower go?

Question

A rower travels upstream at 6km/h and back to the starting place at 10km/h. The total journey takes 48 minutes. How far upstream did the rower go?

Answer 1

Note:  we need all units to match.

Everything should be in either

minutes or hours.

 

(10km/hr)(1/60 hr/min) = 10/60 km/min

1/6 km/min

 

(6 km/hr)(1/60 hr/min) = 1/10 km/min

 

If we go x minutes upstream

we go 48-x minutes back downstream.

 

distance = rate x time ... d = rt

 

d = (1/10)(x) _______ upstream

d = (1/6)(48-x) _____ downstream

 

Since the distance is the same, set

the equations equal to each other 

and solve for x, time upstream.

 

x/10 = (48-x)/6

clear fractions by multiplying

by least common multiple, 30

 

30(x/10) = 30[(48-x)/6]

3x = 5(48-x)

3x = 240 - 5x

8x = 240

x = 30 ... time rowing upstream

 

48-x = 48-30 = 18 mins downstream

 

Distance upstream = x/10

= 30/10 = 3 km

 

check: distance downstream should

also be 3 km

 

(48-x)/6 = 18/6 = 3 km