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zvonat [6]
3 years ago
14

A car motercycle leaves at noon from the same location, heading in the same direction. The average speed of the car is 30mph slo

wer than twice the speed of the motorcycle.
Mathematics
1 answer:
alina1380 [7]3 years ago
8 0

Answer:

speed of motorcycle = 40 mph

speed of car = 50 mph

Step-by-step explanation:

Here is the complete question

A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 mph slower than twice the speed of the motorcycle. In two hours, the car is 20 miles ahead of the motorcycle. Find the speed of both the car and the motorcycle, in miles per hour.

Speed = distance / time

This question would be solved using simultaneous equation

let m =  average speed of the motorcycle

c = average speed of the car

c = 2m - 30  equation 1

20 =(c - m) x 2 equation 2

insert equation 1 into equation 2 and divide through by 2

10 = (2m - 30) - m

solve for m

m = 40 mph

substitute for m in equation 1

2(40) - 20 = 50 mph

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Answer:

A. "an arithmetic sequence with a common difference (d) of -6."

B. 33 hours

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Step-by-step explanation:

A.

Since the sequence lessens by 6, this is an arithmetic sequence with a common difference (d) of -6.

B.

The formula for term of arithmetic sequence is:

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C.

We will use the arithmetic sequence term formula written above, that is:

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D.

We plug in 40 into n and find the hours left:

a_{40}=225+(40-1)(-6)\\a_{40}=225-234\\a_{40}=-9

THis term is NEGATIVE, which means that Greta will not have to work 40 weeks to fulfill the target of 225 hours. She needs to work less.

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