# Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 7/8 of the route, and swims the rest of the way. She swims 0.9 miles. Find the total distance of the triathlon route.

## I suspect a typo, since 4/5 + 7/8 > 1

Now, if you meant to say she ran 7/8 of the way from the cycled part to the end, then
4/5 x + 7/8 * 1/5 x + 9/10 = x
x = 36
check:
4/5 * 36 = 28.8
7/8 * (36-28.8) = 6.3
28.8+6.3+0.9 = 36.0

## Well, let's calculate the distance of the route. Alyssa swims the rest of the way, which is 0.1 miles. So, if we add up the distance she cycles and runs, we get (4/5 + 7/8) miles.

Now, let's find a common denominator for 5 and 8, which is 40.

(4/5) * (8/8) = (32/40)
(7/8) * (5/5) = (35/40)

Adding the fractions together, we get (32/40 + 35/40) = (67/40) miles.

Now, let's add the distance she swam, which is 0.1 miles, to (67/40) miles.

(67/40) + (0.1) = (67/40) + (4/40)

Now, adding the fractions, we get (67/40 + 4/40) = (71/40) miles.

So, the total distance of the triathlon route is 71/40 miles. However, I must warn you, these calculations are a bit fishy. Maybe Alyssa swam with dolphins instead of kilometers? Who knows!

## To find the total distance of the triathlon route, we need to add the distances covered during cycling, running, and swimming.

Alyssa cycles 4/5 of the route, so the distance she cycles is 4/5 times the total distance of the route.

Similarly, Alyssa runs 7/8 of the route, so the distance she runs is 7/8 times the total distance of the route.

Since she cycles and runs a part of the route, the remaining distance of the route will be covered by swimming. It is given that she swims 0.9 miles.

Let's assume that the total distance of the triathlon route is D miles.

Therefore, the distance she cycles = (4/5) * D miles
The distance she runs = (7/8) * D miles
The distance she swims = 0.9 miles

The total distance of the triathlon route = distance cycled + distance run + distance swum
= (4/5) * D + (7/8) * D + 0.9

To find D, we can set up an equation and solve it.

(4/5) * D + (7/8) * D + 0.9 = D

Multiplying both sides of the equation by 40, to get rid of the denominators:

32D + 35D + 36 = 40D

Simplifying the equation:

67D + 36 = 40D

Subtracting 40D from both sides:

27D + 36 = 0

Now, subtracting 36 from both sides:

27D = -36

Finally, dividing both sides by 27:

D = -36/27

Therefore, the total distance of the triathlon route is -36/27 miles.

Since distances cannot be negative, it seems there may have been an error or inconsistency in the problem. Please double-check the given information or rephrase the question if necessary.