A motorboat can maintain a constant speed of 28 miles per hour relative to the water. The boat makes a trip
upstream to a certain point in 35 minutes; the return trip
takes 21 minutes. What is the speed of the current?

7mph

Step-by-step explanation:

Given

Time Taken to go upstream Tup = 35 min

Time Taken to go downstream Tdown=21 min.

Let the absolute speed (i.e speed relative to the stationary riverbed) be :

Vup : going upstream

Vdown: going downstream.

We know that the distance traveled upstream = distance traveled downstream, hence we can equate both distances, i.e. :

Distance Traveled Upstream = Distance Traveled Downstream

Vup · Tup = Vdown · Tdown   (substituting the values for time above)

35Vup = 21Vdown

Vup = (21/35) Vdown (eq 1)

We are also given that the motorboat can travel at V = 28 mph relative to the water.

Since going upstream, we are going AGAINST the current, relative to the riverbed, we expect to be travelling slower. In fact, the absolute difference between the speed relative to the water (i.e V = 28 mph) and the speed relative to the seabed (i.e Vup), is equal to the speed of the current.

The same can be said for going downstream WITH the current, that the absolute difference between V = 28mph and Vdown is also equal to the speed of the current.

Hence we can equate the two:

28 - Vup = Vdown - 28

Vup + Vdown = 2(28)

Vup + Vdown = 56 (eq 2)

If we solve the system of equations (eq 1) and (eq2), we will get

Vup = 21 mph and Vdown = 35 mph

(sanity check tells us that this makes sense because we expect to be going slower upstream because we are going against the current)

Hence current speed

= 28-Vup

= 28 - 21

= 7 mph. (answer)

Sanity Check:

Current speed can also be written:

= Vdown-28

= 35 - 28

= 7 mph (same as what we found above, so this checks out)

answer(s):

4 : 186

278 : 3610

4512 : 5414

6316 : 7218

8120 : 9022

9924 : 10826

11728 : 12630

13532 : 14434

15336 : 16238

17140 : 18042

18944 : 19846

20748 : 21650

22552 : 23454

24356 : 25258

26160 : 27062

27964 : 28866

29768 : 30670

31572 : 32474

33376 : 34278

35180 : 36082

36984 : 37886

38788 : 39690

40592 : 41494

42396 : 43298

441100 : 450102

459104 : 468106

477108 : 486110

495112 : 504114

513116 : 522118

531120 : 540122

549124 : 558126

567128 : 576130

585132 : 594134

603136 : 612138

621140 : 630142

639144 : 648146

657148 : 666150

675152 : 684154

693156 : 702158

711160 : 720162

729164 : 738166

747168 : 756170

765172 : 774174

783176 : 792178

801180 : 810182

819184 : 828186

837188 : 846190

855192 : 864194

873196 : 882198

891200 : 900

hope it ! : d