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Five runners together complete a 100-mile endurance race by running separate, non-overlapping portions of the course. Runner B's portion is 1.5 times the length of Runner A's portion. The combined portion for Runners C and D is twice the length of the combined portion for Runners A and B. Runner E then runs the last 10 miles of the race. How many miles did Runner B run?

 Dec 24, 2020
 #1
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Distance = Rate x Time

 

Runner B ran 75 miles.

 Dec 24, 2020
 #2
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A

B = 1.5 A

C+D  = 2 (A+ 1.5A)

E = 10  

 

Totaled = 100

 

A + 1.5A + 2(A + 1.5A) + 10 = 100

7.5 A + 10 = 100

A = 12

   Then B = 1.5 A = 1.5 (12) = 18 miles

 Dec 24, 2020

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