Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster than his ru

Question

Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster than his running speed. What is his running speed?

in progress 0
Josephine 1 week 2021-11-26T05:52:49+00:00 1 Answer 0

Answers ( )

    0
    2021-11-26T05:54:20+00:00

    Answer:

    Step-by-step explanation:

    Given as :

    The distance cover while running = D_1 = 5 miles

    Let The speed for running = S_1

    The distance cover with bike = D_2 = 80 miles

    The speed for biking = S_2 = 15 mph +  S_1

    Total Time taken = 5 hours

    Now Time = \dfrac{\textrm Distance}{\textrm Speed}

    ∴ 5 hour = \frac{D_1}{S_1} +  \frac{D_2}{S_2}

    Or,  5 hour = \frac{5}{S_1} +  \frac{80}{15+S_1}

    Or, 5 hour = \frac{75 + 5 S_1 + 80 S_1}{S_1(15+S_1)}

    or,  5 × (S_1^{2}+15 S_1) = 85 S_1 + 75

    Or, 5 S_1^{2} + 75 S_1 –  85 S_1 - 75 = 0

    or, 5 S_1^{2} -10 S_1 - 75 = 0

    or,    S_1^{2} -2 S_1 - 15 = 0

    Or, S_1^{2} -3 S_1 + 5 S_1- 15 = 0

    Or, S_1 (S_1 - 3) + 5 (S_1 - 3) = 0

    Or, (S_1 - 3) ( S_1 + 5 ) = 0

    S_1 = 3 , – 5

    So, the running speed = 3 mile per hour

    And the biking speed = 15 mph + 3 mph = 18 mile per hour

    Hence The running speed of Stu is 3 mile per hour  .  Answer

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )