The distance on a bike path between Westfield and Southborough is 46 mi. Tracey leaves Westfield heading to Southborough cycling at a constant rate of 15 mph. Emma leaves her house at the same time and cycles along the same path from Southborough to meet Tracey. Her cycling rate is 8 mph. How many hours will it take until the two friends meet along the bike path?

their combined speed is 15+8 = 23 mi/hr

so, they will cover the 46 miles in 2 hours.

time = distance/speed

To find out how many hours it will take for Tracey and Emma to meet along the bike path, we need to determine the time it would take for Tracey and Emma to cover the same distance.

We know that Tracey's speed is 15 mph and Emma's speed is 8 mph. Since they are both cycling towards each other, their combined speed would be the sum of their individual speeds, which is 15 mph + 8 mph = 23 mph.

The distance between Westfield and Southborough is given as 46 miles. To find the time, we can use the formula:

Time = Distance / Speed

Plugging in the values:

Time = 46 miles / 23 mph = 2 hours

Therefore, it will take Tracey and Emma approximately 2 hours to meet each other along the bike path.

To find out how many hours it will take for Tracey and Emma to meet along the bike path, we can first calculate how long it will take Tracey to cover the entire distance.

We know that Tracey is cycling at a constant rate of 15 mph, and the distance between Westfield and Southborough is 46 miles.

To find the time it will take Tracey, we can use the formula:

Time = Distance / Rate

So, the time it will take for Tracey to cover the whole distance is:

Time = 46 miles / 15 mph

Time = 3.07 hours (rounded to the nearest hundredth)

Now, since Emma is cycling towards Tracey from the opposite direction, we can use the same formula to find out how long it will take for her to cover the same distance.

Emma's cycling rate is 8 mph, and the distance is still 46 miles.

Time = 46 miles / 8 mph

Time = 5.75 hours (rounded to the nearest hundredth)

Therefore, it will take 3.07 hours for Tracey and 5.75 hours for Emma to meet along the bike path after they both start cycling.