MATH SOLVE

2 months ago

Q:
# The time t required to drive a certain distance varies inversely with the speed r. If it takes 2 hours to drive the distance at 30 miles per hour, how long will it take to drive the same distance at 35miles per hour?

Accepted Solution

A:

β΅ To simply this and put it in other words, the time (t) required to drive a certain distance varies inversely with the speed (r), which means that it is going to take less time to drive to a certain place if the speed is faster and it is going to take more time to drive to the same place if the speed is slower!

βΆ Now that we understand that, lets see what information we have :

β It takes 2 hours to drive the distance if the speed is 30 miles per hour

β· Now we want to know how long it would take to drive the same distance if we increase the speed to 35 miles per hour instead of 30 miles per hour!

β Remember #β΅ : If we increase the speed, that means that it is going to take less time to drive the same distance!

βΈ This situation is inversely proportional, which means that one value decreases at the same rate that the other increases.

Lets work with βtβ and βrβ :

β t is inversely proportional to r

β t is directly proportional to 1/r

Which means that :

β t = Γ/r

(βΓβ being the constant of proportionality)

βΉ Knowing that, letβs replace everything we know in the equation to find the constant of proportionality (Γ) :

t = 2 hours (120 minutes)

r = 30 miles per hour

β

2 = Γ/30 OR 120 = Γ/30

β

2 = Γ/30 OR 120 = Γ/30

x30 x30 x30 x30

β

60 = Γ OR 3600 = Γ

Γ = 60 Γ = 3600

β So now we know that : t = 60/r (if we use hours)

β So now we know that : t = 3600/r (if we use minutes)

βΊ Now we can use this equation to find the answer to find out how ling it would take to drive the same distance distance at 35 miles per hour :

t = ?

r = 35 miles per hour

β

t = 3600/35

β

t = 102.857143

β So if we round up, βtβ would equal about 102 minutes and 86 second, which means about 103 minutes and 26 seconds, which also means about 1 hour and 7 minutes!

β So the final answer would be :

It will take about 1 hour and 7 minutes to drive the same distance at 35 miles per hour!

I really hope this helped, if thereβs anything just let me know! β»

βΆ Now that we understand that, lets see what information we have :

β It takes 2 hours to drive the distance if the speed is 30 miles per hour

β· Now we want to know how long it would take to drive the same distance if we increase the speed to 35 miles per hour instead of 30 miles per hour!

β Remember #β΅ : If we increase the speed, that means that it is going to take less time to drive the same distance!

βΈ This situation is inversely proportional, which means that one value decreases at the same rate that the other increases.

Lets work with βtβ and βrβ :

β t is inversely proportional to r

β t is directly proportional to 1/r

Which means that :

β t = Γ/r

(βΓβ being the constant of proportionality)

βΉ Knowing that, letβs replace everything we know in the equation to find the constant of proportionality (Γ) :

t = 2 hours (120 minutes)

r = 30 miles per hour

β

2 = Γ/30 OR 120 = Γ/30

β

2 = Γ/30 OR 120 = Γ/30

x30 x30 x30 x30

β

60 = Γ OR 3600 = Γ

Γ = 60 Γ = 3600

β So now we know that : t = 60/r (if we use hours)

β So now we know that : t = 3600/r (if we use minutes)

βΊ Now we can use this equation to find the answer to find out how ling it would take to drive the same distance distance at 35 miles per hour :

t = ?

r = 35 miles per hour

β

t = 3600/35

β

t = 102.857143

β So if we round up, βtβ would equal about 102 minutes and 86 second, which means about 103 minutes and 26 seconds, which also means about 1 hour and 7 minutes!

β So the final answer would be :

It will take about 1 hour and 7 minutes to drive the same distance at 35 miles per hour!

I really hope this helped, if thereβs anything just let me know! β»