Question

PLEASE HELP!!! Two towns are 1100 miles apart. A group of hikers starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels one half mile per hour slower than the other​ group, find the rate of each group.

Answer 1

Answer:

2.54 miles/hr

2.04 miles/hr

Step-by-step explanation:

Given: Distance between the two towns = 1100 miles

Difference between speeds = $\frac{1}{2}$ miles/hr

Total time when they meet = 240 hours

To find:

Let distance traveled by first group = $x$ miles.

Now, the distance traveled by second group = (1100-$x$) miles/hr

The relation between Speed, Time and Distance is given as:

$\text{Speed =} \dfrac{\text{Distance}}{\text{Time}}$

Let speed of first group = $S_1$

$S_1 = \dfrac{x}{240}$

Let speed of second group = $S_2$

$S_2 = \dfrac{1100-x}{240}$

As per question, $S_1$ = $S_2$ + $\frac{1}{2}$

$\dfrac{x}{240} = \dfrac{1100-x}{240} + \dfrac{1}{2}\\\Rightarrow \dfrac{x}{240} - \dfrac{1100-x}{240} = \dfrac{1}{2}\\\Rightarrow \dfrac{x-1100+x}{240} = \dfrac{1}{2}\\\Rightarrow 2x - 1100 = 120\\\Rightarrow 2x = 1220\\\Rightarrow x = 610 ft$

Now,

$S_1 = \dfrac{x}{240}$

Putting value of $x$:

$S_1 = \dfrac{610}{240}\\\Rightarrow S_1 = 2.54\ miles/hr$

Similarly, putting value of $x$ in $S_2$:

$S_2 = \dfrac{1100-610}{240}\\\Rightarrow S_2=\dfrac{490}{240}\\\Rightarrow S_2 = 2.04\ miles/hr$