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?

Answer 1

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