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OleMash [197]
3 years ago
7

Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other, and the

y meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists? Put both values in the answerbox, separated with a comma, and select the appropriate units.
Mathematics
1 answer:
Iteru [2.4K]3 years ago
5 0

Answer:

Speed of a= 21 miles/hr

r = Speed of b= 7 miles/hr

Speed of a = 3r

Step-by-step explanation:

The cyclist are 112 miles apart

Time traveled by two = 4 hours

Speed of a = 3 * speed of b

If a cylcles 3 times More than b, then a will cover 3*distance of b

But speed = distance/time

Time = 4hours

Total distance=112

a = 3b

3b + b = 112

4b = 112

b = 112/4

b = 28 miles

a = 3b

a = 3*28

a = 84 Miles

They bought traveled 4 hours

Speed of a = 84miles/4 hours

Speed of a= 21 miles/hr

Speed of b = 28miles/4 hours

Speed of b = 7 miles/hr

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Answer:

a) Sketch the graph of the function f. (it is in the attached file)

b) What was the ratio at the beginning of 2006? At the beginning of 2014?

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For 2014 the ratio is 3.5

c) Over what years is the ratio constant?

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d) Over what years is the decline of the ratio greatest?

[2010, 2030]

Step-by-step explanation:

b) We first need to know in between which function 2006 falls into, so if we start in t=0=1995, then 2006-1995=11, t=11

t=11 fall into:

f(x)=-0.03t+4.25

f(11)=-0.03(11)+4.25=3.92

For 2006 the ratio is 3.92

2014:

Same process that 2006, t=0=1995, then 2014-1995=19, t=19

t=19fall into:

f(x)=-0.075t+4.925

f(19)=-0.075(11)+4.925=3.5

For 2014 the ratio is 3.5

c) The ratio is only constant in the first section of the graph 0≤t<5, since 4.1 is constant. Following the same process for the years in star (b) we have t=0, 1995+0=1995, t=5, 1995+5=2000.

The ratio will be constant between [1995, 2000]

d) For the greatest decline we need to compare slopes. From the line equation we have:

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f(x)=-0.03t+4.25  for 5≤t<15

f(x)=-0.075t+4.925  for 15≤t≤35

So:

m=-0.03 for 5≤t<15

m=-0.075 for 15≤t≤35

If we are measuring the steepness of the decline, we have to compare:

|-0.03| and |-0.075| or 0.03 and 0.075, easily finding that 0.075>0.03

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t=15, 1995+15=2010, and t=35, 1995+35=2030

This means that the biggest decline is between the years:

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When Mohammed was born, the baby was 21 inches tall. at his last check up, he was 38 inches tall. what is the percent increase i
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80.95

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