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.
Please help me solve it
To find the total distance of the triathlon route, we need to add up the distances Alyssa cycled, ran, and swam.
Given that Alyssa cycles 4/5 of the route and runs 7/8 of the route, we can express these distances as fractions of the total distance.
Let's say the total distance of the triathlon route is D miles.
The distance Alyssa cycled can be calculated as (4/5) * D miles, and the distance she ran can be calculated as (7/8) * D miles.
The distance she swam is given as 0.9 miles.
To find the value of D, we can set up the equation:
(4/5) * D + (7/8) * D + 0.9 = D
Now, let's solve the equation:
(4/5) * D + (7/8) * D + 0.9 = D
Multiplying 5 on both sides to eliminate the fraction in the first term:
4D + (35/8) * D + 4.5 = 5D
Multiplying 8 on both sides to eliminate the fraction in the second term:
32D + 35D + 36 = 40D
Rearranging the equation:
40D - 35D - 32D = 36
3D = 36
Dividing both sides by 3:
D = 36 / 3
D = 12
So, the total distance of the triathlon route is 12 miles.