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11111nata11111 [884]
3 years ago
8

Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your

Mathematics
2 answers:
Alinara [238K]3 years ago
6 0

Answer:

The distance from my house to friend's house is 14 miles

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- Driving to the friend's house rate is 35 miles per hour

- Driving to my home rate is 40 miles per hour

- The round trip took 45 minutes

- We need to find the distance from my house to my friend's house

* <em>At first lets change 45 minutes to hour because the rate of driving</em>

<em>  unit is miles per hour</em>

∵ 1 hour = 60 minutes

∴ 45 minutes = \frac{45}{60}=\frac{3}{4} hour

- <em>Assume that the distance from my house to friend's house is d,</em>

<em>  the time for the trip from my house to the friend's house is</em> t_{1}

 <em>and the time from friend's house to my house is</em> t_{2}

∵ The distance between the two houses is d

∵ Distance = rate of driving × time of the trip

∴ d = 35 × t_{1} = 35t_{1}

∴ d = 40 × t_{2} = 40t_{2}

- <u><em>Equate the two equations</em></u>

∴ 35t_{1} = 40t_{2}

- Divide both sides by 35

∴ t_{1}=\frac{40}{35}t_{2}=\frac{8}{7}t_{2}

∴ t_{1}=\frac{3}{4}t_{2} ⇒ (1)

- The time of the round trip is \frac{3}{4} hour

∴ t_{1}+t_{2}=\frac{3}{4} ⇒ (2)

- <u><em>Substitute equation (1) in equation (2)</em></u>

∴ \frac{8}{7}t_{2}+t_{2}=\frac{3}{4}

∴ \frac{15}{7}t_{2}=\frac{3}{4}

- Divide Both sides by \frac{15}{7}

∴ t_{2}=0.35 hour

∵ d =  40t_{2}

- Substitute the value of t_{2} in the equation above

∴ d = 40(0.35) = 14

∵ <u><em>d represents the distance from my house to friend's house</em></u>

∴ The distance from my house to friend's house is 14 miles

Mamont248 [21]3 years ago
4 0

Answer:

14 miles.

Step-by-step explanation:

Let the distance traveled from home to destination = x miles.

Speed while going to friend's house = 35 miles per hour.

Speed while coming back = 40 miles per hour.

Total Time taken for the journey = 45 minutes = 0.75 hours.

Let the time taken while going to friend's house = y hours.

Therefore, the time taken while going to friend's house = (0.75 - y) hours.

To find x and y, model the speeds of both the journeys.

Speed while going to friend's house = Distance/Time.

35 = x/y.

x = 35y (Equation 1).

Speed while coming back = Distance/Time.

40 = x/(0.75 - y).

x = 40(0.75 - y) (Equation 2).

Since x = x, therefore:

35y = 30 - 40y.

75y = 30.

y = 30/75.

y = 0.4 hours.

Put y = 0.4 hours in Equation 1:

x = 35y.

x = 35(0.4).

x = 14.

Therefore, the distance between my friend's house and my house is 14 miles!!!

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