A boat on a river traveled from City A to City C with a stop at City B. On the first part of the trip, the boat traveled at an average speed of 10 miles per hour. From City B to City C the average speed was 15 miles per hour. The entire trip covered 100 miles. How long did the entire trip take if the two parts each took the same number of hours?
I don't understand how to solve this question.
Well, let's see if I can float you an answer that makes this question a little less choppy. We know that the boat traveled at an average speed of 10 miles per hour for the first part of the trip, and at 15 miles per hour for the second part. And we also know that both parts took the same number of hours.
So, let's call the time it took for each part of the trip "x" hours. This means that the first part also took "x" hours, and the second part also took "x" hours.
Now, since the boat traveled at 10 miles per hour for the first part of the trip, we can say that the distance traveled in the first part is 10 times "x", which is 10x miles.
Similarly, for the second part of the trip, the boat traveled at 15 miles per hour, so the distance covered in that part would be 15 times "x", which is 15x miles.
And since the entire trip covered 100 miles, we can express this with an equation:
10x + 15x = 100.
Combining the like terms, we get:
25x = 100.
And if we divide both sides by 25, we find that x = 4.
So, the trip took "x" hours for each part, which means it took 4 hours for the boat to travel from City A to City C with a stop at City B.
Hope that clarifies things and doesn't make you seasick!
To solve this question, we can set up a system of equations based on the information given.
Let's say the time taken for the first part of the trip (from City A to City B) is 't' hours. So the time taken for the second part (from City B to City C) is also 't' hours.
Now let's calculate the distances traveled for each part of the trip.
Distance traveled in the first part = Speed * Time
Distance traveled in the second part = Speed * Time
Given:
Speed of the first part = 10 miles per hour
Speed of the second part = 15 miles per hour
Total distance of the trip = 100 miles
Using the formula Distance = Speed * Time, we can write the following equations:
10t + 15t = 100
Combining the like terms, we get:
25t = 100
Now, we can solve this equation to find the value of 't':
t = 100 / 25
t = 4
Therefore, each part of the trip took 4 hours. Since the total time is the sum of the times for both parts, the entire trip took:
Total time = Time for first part + Time for second part
Total time = t + t
Total time = 4 + 4
Total time = 8 hours
So, the entire trip took 8 hours.
Would have preferred that 8 hours answer without the question mark behind it.
Trust your math!!
8 hours?
let the distance from A to B be x miles
let the distance from B to C be 100-x
I used to have my students create a chart for these, made up of 3 columns
distance, rate and time for the columns, remember: dist = rate x time
so when 2 entries are in, the 3rd can be found
On the side we would state the cases, here the two cases are:
------------------ Dist ......rate......time
from A to B |... x ......|..10 ...|... x/10
from B to A |..100-x .|..15 ...|.. (100-x)/15 , hope this lines up somehow
but the two times are equal
x/10 = (100-x)/15
cross-multiply
15x = 1000 - 10x
25x = 1000
x = 40
Finish it up, filling in the missing parts in the chart