Two families met at a par for a picnic at the end of the day, they part ways. Family A leaves 15 minutes after Family B and travels east at an average of 42 mph; while family B travels west at an average of 50mph. Both families have an approximately 160 miles to travel.
1.)find the time(in hours and minutes) that it takes them to be 120 miles apart
2.) when family B arrives at home how much further does Family A still have to travel?
I believe the answer to part 1 is 8 hours and 9 minutes but i have no idea for the second part on how to set up the equation. For the first part i made a table with R,T,D and for the second part i also made a table with R,T,D
they are moving apart at 92 mph (the sum of their speeds)
so it takes ... 120 mi / 92 mph ... for them to be 120 mi apart
B arrives home in ... 160 mi / 50 mph
use B's travel time (minus 15 min) to find how far A has traveled
so would the equation for b be
42(x-15)=160-50x
B's travel time is ... 160/50 = 3.2 hr
at this point, A has been traveling for
... 3.2 - .25 = 2.95 hr
A's remaining distance is
... 160 - (42 * 2.95)
To find the time it takes for the two families to be 120 miles apart, you can set up an equation based on the distance traveled by both families.
Let's consider the time it takes for Family A to travel 120 miles and Family B to travel 120 miles. Since family A travels east and family B travels west, their total distances will add up to the total separation.
Here's how you can set up the equation:
Family A's distance = Family A's rate × Family A's time
Family B's distance = Family B's rate × Family B's time
Since both families are traveling the same distance of 120 miles, we can set these two equations equal to each other:
42 × (t + 15 minutes) = 50 × t
Let's solve this equation to find the time it takes for them to be 120 miles apart:
42(t + 15/60) = 50t
42t + 10.5 = 50t
10.5 = 8t
t ≈ 1.3125 hours
To convert this to hours and minutes, multiply the decimal part (0.3125) by 60 to get the minutes:
0.3125 × 60 = 18.75 minutes ≈ 19 minutes
Therefore, it takes about 1 hour and 19 minutes for the two families to be 120 miles apart.
Now let's move on to the second part of the question:
To find how much further Family A has to travel when Family B arrives home, we need to calculate the distance Family B travels before reaching home.
The total distance both families need to travel is approximately 160 miles. Since Family B is traveling west, its distance to reach home is equal to the total distance minus the distance it traveled to be 120 miles apart from Family A.
Distance traveled by Family B = Total distance - Distance traveled to be 120 miles apart
Distance traveled by Family B = 160 miles - 120 miles
Distance traveled by Family B = 40 miles
Therefore, when Family B arrives home, Family A still has to travel an additional 40 miles.