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 $64$ $"km/h"$ .