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 belive the answer to part 1 is 8 hours and 9 minutes but i have no idea for the second on how to set up the equation. For the first part i made a table with R,T,D and for the second one i also made a table with R,T,D
I just need to know the equation for Part 2 in order to solve the problem
To solve this problem, we can use the formula Distance = Rate × Time.
1.) To find the time it takes for family A and family B to be 120 miles apart, we need to set up two separate equations using the given information:
For family A: Distance_A = Rate_A × Time_A
For family B: Distance_B = Rate_B × Time_B
Let's calculate the time for both families:
Distance_A = 120 miles
Rate_A = 42 mph
Time_A = Distance_A / Rate_A = 120 / 42 ≈ 2.857 hours
Distance_B = 120 miles
Rate_B = 50 mph
Time_B = Distance_B / Rate_B = 120 / 50 = 2.4 hours
However, since Family A left 15 minutes (0.25 hours) after Family B, we need to adjust the time for Family A:
Adjusted_Time_A = Time_A + 0.25 hours = 3.107 hours
To convert this adjusted time to hours and minutes, we have:
Hours = 3
Minutes = (0.107 hours) × 60 ≈ 6.42 minutes
Rounded to the nearest whole number, the answer is 3 hours and 6 minutes.
Therefore, the correct answer for part 1 is 3 hours and 6 minutes.
2.) To find out how much further Family A still has to travel when Family B arrives home, we can calculate the distance Family B traveled using the formula:
Distance_B = Rate_B × Time_B
Distance_B = 50 mph × Time_B = 50 mph × 2.4 hours = 120 miles
Since both families originally had 160 miles to travel, this means that Family A has 160 - 120 = 40 miles remaining.
Therefore, the correct answer for part 2 is that Family A still has 40 miles left to travel when Family B arrives home.