Phoebe is swimming in the ocean, 187 meters out from the beach. She screams for help and starts swimming for the beach at 0.7 meters per second. 15 seconds later Calvin starts toward her in a rowboat, going 1.6 meters per second. Let x be the number of seconds since Phoebe screamed. a. Draw a diagram showing the beach where Calvin starts and the point 187m away where Phoebe starts. Show Calvin and Phoebe somewhere in between. b. Write an expression for the distance Phoebe has gone and add to diagram. c. Write an expression for the distance Phoebe is from the beach and add to diagram. d. Write an expression for the number of seconds Calvin has been rowing. e. Write an expression for Calvin's distance from the beach and add to diagram. f. How far apart will they be 33 seconds after Phoebe screamed? g. How far from the beach with they be when Calvin reaches Phoebe(Find how long it takes to reach her first).
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a. Diagram:
| Calvin
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|
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| Phoebe (x seconds)
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| Beach
b. Expression for the distance Phoebe has gone:
The distance Phoebe has gone in x seconds can be calculated using the formula:
Distance = Speed × Time
In this case, Phoebe's speed is 0.7 meters per second, and the time is x seconds. Therefore, the expression for Phoebe's distance is 0.7x.
c. Expression for the distance Phoebe is from the beach:
Since Phoebe starts 187 meters out from the beach and the distance she has gone is 0.7x, we can subtract the distance she has gone from the initial distance to find the remaining distance from the beach. Therefore, the expression for the distance Phoebe is from the beach is 187 - 0.7x.
d. Expression for the number of seconds Calvin has been rowing:
Calvin starts 15 seconds after Phoebe screamed, so the number of seconds Calvin has been rowing is (x - 15).
e. Expression for Calvin's distance from the beach:
Calvin's speed is 1.6 meters per second, and the time he has been rowing is (x - 15) seconds. Therefore, the expression for Calvin's distance from the beach is 1.6(x - 15).
f. To find how far apart they will be 33 seconds after Phoebe screamed, we need to calculate their distances from the beach at that time.
Phoebe's distance from the beach after 33 seconds: 187 - 0.7(33)
Calvin's distance from the beach after 33 seconds: 1.6(33 - 15)
Subtract Phoebe's distance from Calvin's distance to find the distance between them.
g. To find how far from the beach they will be when Calvin reaches Phoebe, you need to find the time at which Calvin reaches Phoebe. Set Phoebe's distance from the beach (187 - 0.7x) equal to Calvin's distance from the beach (1.6(x - 15)), and solve for x. Then substitute the value of x in either Phoebe's or Calvin's distance expression to find how far from the beach they will be when Calvin reaches Phoebe.