A cyclist is going at 4 kmph and takes them #t# less than #14# hours to get to their destination. On the trip back they take the same route, but at #10 kmph# and make it back in #t# hours. Using a diagram, how do you find the value of #t#?

Question

A cyclist is going at 4 kmph and takes them #t# less than #14# hours to get to their destination.  On the trip back they take the same route, but at #10 kmph# and make it back in #t# hours.  Using a diagram, how do you find the value of #t#?

Kennedy Adams · Accepted Answer

Here's your diagram

The formula for speed is #S = d/t#. However, we can rearrange it so that #S xx t = d#. Thus, speed • time = distance.

#4(14 - t) = 10(t)#

#56 - 4t = 10t#

#56 = 14t#

#4 = t#

Thus, it took her 4 hours to bike and 10 hours to walk.

Therefore, the distance is 40 kilometres, since #10 xx 4 = 40#

Hopefully this helps!

Jace Anderson · Answer

undefined You can use a distance-time diagram to represent the two trips. Since the distance is the same for both trips, you can set up an equation where the distance equals the speed multiplied by the time. Then, solve for t.

Jameson Allen · Answer

undefined To find the value of t, we can use the formula:

Distance = Speed × Time

Since the distance traveled in both directions is the same, we can set up the equation:

Distance (going) = Distance (returning)

Using the formula:

Speed × Time (going) = Speed × Time (returning)

Given that the cyclist goes at 4 kmph on the trip there and 10 kmph on the trip back, and that it takes less than 14 hours to get to the destination and t hours to return, we can set up the equation as follows:

4 × (14 - t) = 10 × t

Now, solve for t.