A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?

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usumbiix · Accepted Answer

Step 1  Change 20 min to 13hr  Change 15 min to 14hr  Let c = rate of the current then  (16−c)= rate uostream  (16+c)= rate downstream  Assume the trip up and the trip back were the same distance  Write a distance equation dist=time×rate  Dist upstream = dist downstream  14(16+c)=13(16−c)  Multiply both sides by 12, to get rid of the denominatros, results:  3(16+c)=4(16−c)  48+3c=64−4c  3c+4c=64−48  7c=16  c=167  c=2.2857∓h is the current  Check solution by finding the distance of each trip (should be equal)  0.25(16+2.2857)=4.57mi  0.333(16−2.2857)=4.57mi

veiga34 · Accepted Answer

Step 1 Let x = speed of the current then (16−x)= speed upstream (16+x)= speed downstream Convert 20 min to hrs 2060=13hrs Convert 15 min to hrs 1560=14hrs Distance of the two trips is the same; write a dist equation: dist=time×speed 14(16+x)=13(16−x) Multiply both sides 12 to get rid of the denominators: 3(16+x)=4(16−x) 48+3x=64−4x 3x+4x=64−48 7x=16 x=167 x∼2.3mph is the current Check solution with a calc, confirm that the distances are equal 0.33×13.7=4.5 0.25×18.3=4.5

alenahelenash · Accepted Answer

Answer:2.29 miles per hourExplanation:When the boat is traveling upstream, its effective speed is reduced by the speed of the current. So the speed relative to the ground is b−c.Given that the boat takes 20 minutes to travel upstream, which is equivalent to 13 hour, we can write the equation:{Distance}={Speed}×{Time}Thus, the distance traveled upstream is (b−c)×13.Similarly, when the boat is traveling downstream, its effective speed is increased by the speed of the current. So the speed relative to the ground is b+c.Given that the boat takes 15 minutes to travel downstream, which is equivalent to 14 hour, we can write the equation:{Distance}={Speed}×{Time}Thus, the distance traveled downstream is (b+c)×14.Since the distance traveled upstream and downstream is the same, we can set up the equation:(b−c)×13=(b+c)×14To solve this equation, we can cross-multiply:4(b−c)=3(b+c)Expanding the equation:4b−4c=3b+3cSimplifying the equation:b=7cTherefore, the speed of the boat relative to the water is 7 times the speed of the current.To find the speed of the current, we can substitute b=16 (since the boat&#039;s speed relative to the water is given as 16 miles per hour) into the equation:16=7cSolving for c:c=167≈2.29{&amp;nbsp;mph}Thus, the speed of the current is approximately 2.29 miles per hour.

star233 · Accepted Answer

1. Speed of the boat relative to the water when going upstream:{Speed}up={Speed}boat−{Speed}current=16−c2. Speed of the boat relative to the water when going downstream:{Speed}down={Speed}boat+{Speed}current=16+cNow, we know that distance = speed × time. Let&#039;s calculate the distances for the upstream and downstream trips.Distance upstream:{Distance}up={Speed}up×{Time}up=(16−c)×2060=203(16−c)Distance downstream:{Distance}down={Speed}down×{Time}down=(16+c)×1560=14(16+c)Since the distance traveled upstream and downstream is the same, we can set the two distances equal to each other:203(16−c)=14(16+c)To solve for c, we can simplify and solve the equation:203(16−c)=14(16+c)Multiply both sides of the equation by 12 to eliminate fractions:80(16−c)=3(16+c)Simplify the equation:1280−80c=48+3cBring the terms with c to one side:80c+3c=1280−4883c=1232Finally, solve for c:c=123283

user_27qwe · Accepted Answer

Let&#039;s denote the speed of the current by x miles per hour.When the motorboat is traveling upstream (against the current), its effective speed relative to the ground is reduced by the speed of the current. So, the speed of the boat upstream is (16−x) miles per hour.We are given that the boat takes 20 minutes (or 2060=13 hours) to reach a certain point upstream. We can use the formula distance=speed×time to calculate the distance covered by the boat:dupstream=(16−x)×13On the return trip downstream (with the current), the effective speed of the boat is increased by the speed of the current. So, the speed of the boat downstream is (16+x) miles per hour.We are given that the boat takes 15 minutes (or 1560=14 hours) to make the return trip. Again, using the distance formula, we can calculate the distance covered by the boat:ddownstream=(16+x)×14Now, since the boat is traveling the same distance in both directions (upstream and downstream) to reach the same point, we can set the two distances equal to each other:(16−x)×13=(16+x)×14To solve for x, we can cross-multiply and simplify the equation:4(16−x)=3(16+x)64−4x=48+3x7x=16x=167Therefore, the speed of the current is 167 miles per hour.

A motorboat can maintain a constant speed of 16 miles

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