Answer – The time taken for the onward trip is found to be 2.9 hours, while the time taken for the return trip is found to be 5.8 hours.

Explanation:

The rate at which an object moves is defined as the total distance covered by it in a particular period of time. So if the object moves at a constant rate, the distance it covers/travels is given by the formula:

$Dis\tan ce traveled d = Rate of movement r Time taken t$

This is known as the distance time rate formula and is often used to solve simple word problems related to speed in math.

To answer the given question, let us begin by considering the distance traveled each way as D.

Since we’re required to find the time taken for the individual trips, we can start by finding the distance traveled during each trip. For this, we modify the distance rate time formula as:

$Time taken= \frac{Dis\tan ce traveled}{Rate of movement}$

$Total time taken =\frac{Dis\tan ce traveled during onward trip}{Rate of movement during onward trip} + \frac{Dis\tan ce traveled during return trip}{Rate of movement during return trip}$

Let’s now substitute the values we know in the above formula:

$8.7 = \frac{D}{80} + \frac{D}{40}$

On simplifying further using the lowest common multiple, we get:

$8.7 = \frac{D + 2D}{80}$

$\Rightarrow 8.7 = \frac{3D}{80}$

$D = \frac{8.7 \times 80}{3} = 2.9 \times 80 =232 miles$

Now that we know the distance traveled during each trip, we can find the time taken for each journey too:

$Time taken for onward trip=\frac{Dis\tan ce traveled during onward trip}{Rate of movement during onward trip} = \frac{232}{80} = 2.9 hours$

Similarly, $Time taken for return trip=\frac{Dis\tan ce traveled during return trip}{Rate of movement during return trip} = \frac{232}{40} = 5.8 hours$

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