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The speed of boat in still water is 24 mph. If the boat travels 54 miles upstream in the same time it takes to

The speed of boat in still water is 24 mph. If the boat travels 54 miles upstream in the same time it takes to travel 90 miles downstream, Find the speed of current.

Public Comments

1. time = distance/speed speed upstream = (24 - c), where c = current speed speed downstream = (24 + c) upstream time = downstream time 54/ (24 - c) = 90 / (24 + c) Cross multiply: 54(24 + c) = 90(24 - c) Divide each side by 18: 3(24 + c) = 5(24 - c) Expand and solve: 72 + 3c = 120 - 5c 72 + 8c = 120 8c = 48 c = 6 mph
2. 40mph
3. I also got 6 mph. 40??? what were you thinking. if current was 40, the boat could never get upstream.
4. let x= speed of water let t = time taken speed of boat = 24 t(24 + x) = 90 t(24-x) = 54 solve each for t t= 90/ (24+x) t= 54/ (24-x) let t= each other 90/(24+x)=54/(24-x) 90(24-x) = 54(24+x) 2160-90x=1296+54x 2160 - 1296 = 54x + 90x 864 = 144x 6 = x check t= 90/ (24+6) t=90/30 3 t= 54/ (24-6) t=54/18 t=3 since t is = the correct speed of river is 6
5. knowns: s(s)=speed of the boat in still water= 24(mph) d(u)=distance travelled going upstream=54 (miles) d(d)=distance travelled going downstream=90 (miles) unknowns: s(u)=speed of the boat going upstream (mph) s(d)=speed of the boat going downstream (mph) s(c)=speed of the current (mph) equations: (1) s(u)=s(s)-s(c)=24-s(c) (2) s(d)=s(s)+s(c)=24+s(c) (3a) s(c)=s(d)-24 (3b) s(c)=24-s(u) (4) st=d (5) t=d/s (6) t=d(u)/s(u)=54/s(u) (7) t=d(d)/s(d)=90/s(d) (8) 54/s(u)=90/s(d) (9) s(d)=1.67s(u) (10) s(c)=s(d)-24=1.67s(u)-24 (11) s(c)=24-s(u) (12) 24-s(u)=1.67s(u)-24 (13) 24+24=1.67 s(u)+s(u) (14) 48={1.67+1} s(u) (15) 48= 2.67 s(u) (16) s(u)=48/2.67=17.98 (17) s(c)=24-s(u)=24-17.98=6.02 (18) s(c)=6.02 (mph) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>problem solved (19) s(u)=24-6.02=17.98 (20) s(d)=24+6.02=30.02 (21) t=d(u)/s(u)=54/s(u)=54/17.98=3.00 (22) t=d(d)/s(d)=90/s(d)=90/30.02=3.00