Answer:
It will take them (Matt and Chris) 0.395 hours to be 64 miles apart
It will take 5.5 hours for the boats to be 66 miles apart
Explanation:
We are to determine the time when Matt and Chris will be 64 miles apart, that is, when the total distance traveled by both of them will be 64 miles.
Let the time be t and
Let the distance covered by Matt be S₁ and the distance covered by Chris be S₂.
For Matt,
From the question, Matt drives at a speed of 79 miles per hour
From the formula
Distance = Speed × Time
S = v × t
∴ S₁ = 79×t
S₁ = 79t
For Chris,
From the question, Chris drives at a speed of 83 miles per hour
Using the same formula,
∴ S₂ = 83 × t
S₂ = 83t
To determine when they will be 64 miles apart, that is when S₁ + S₂ = 64 miles.
Hence,
S₁ + S₂ = 79t + 83t
∴64 = 79t + 83t
64 = 162t
t = 64/162
t = 0.395 hours
Hence, it will take them 0.395 hours to be 64 miles apart.
For the boats,
To determine how many hours it will take them to be 66 miles apart, that is when the total distance traveled by the two boats will be 66 miles.
Let the time be t and
Let the distance traveled by the northbound boat be S₁ and the distance traveled by the southbound both be S₂.
From the question,
The northbound boat travels five miles per hour
From the formula
Velocity = Distance / Time
Then, Distance = Velocity × Time
That is, S = v × t
Hence, for the northbound boat,
S = S₁
v = 5 miles per hour
∴ S₁ = 5t
Also from the question,
The southbound boat goes seven miles per hour
Hence, for the southbound boat
S = S₂
v = 7 miles per hour
∴ S₂ = 7t
To determine when the boats will be 66 miles apart, that is when S₁ + S₂ = 66 miles
Then,
S₁ + S₂ = 5t + 7t
Hence,
66 = 5t + 7t
66 = 12t
t = 66/12
t = 5.5 hours
Hence, it will take 5.5 hours for the boats to be 66 miles apart.