Question

Josue is running intervals. If he runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds, how many of each type of interval did he run?

Answer 1

Answer: He run 7 high-speed intervals and 8 low-speed intervals.

Step-by-step explanation:

Let x = Number of high-speed intervals.

y= Number of low-speed intervals .

He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.

4 min 56 sec = (4(60)+56) sec = 296  sec   [ 1 minute = 60 seconds]

According to the question , we have the following linear equations :

$x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)$

Multiply (i)by 16 , we get

$16x+16y=240\ ...(iii)$

Subtract (iii) from (ii)

$7y=56\\\\\Rightarrow\ y=8$

Put value of y in (i) , we get

$x+8=15\Rightarrow\ x=7$

Hence, he run 7 high-speed intervals and 8 low-speed intervals.