Time varies inversely with speed if the distance is constant. A trip takes 4 hours at 80 km/h. How long does it take at 64 km/h?

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Answer 1 · 2017-08-27T09:30:01

#5# hours

When two variables are inversely proportional, their product is equal to a constant.

In this case, #"distance"# #=# #"time"# #times# #"speed"#.

We are given the fact that the "trip takes #4# #"h"# at #80# #"km/h"#".

Let's substitute these values into the equation:

#Rightarrow "Distance" = 4# #"h" times 80# #"km/h"#

#therefore "Distance" = 320# #"km"#

So the total distance of the trip is #320# #"km"#.

Let's find out how long it takes to travel this distance at #64# #"km/h"#:

#Rightarrow 320# #"km"# #=# #"time" times 64# #"km/h"#

#Rightarrow frac(320 " km")(64 " km/h") = "Time"#

#therefore "Time" = 5# #"h"#

Therefore, the trip takes #5# hours at #64# #"km/h"#.