Sarah starts at a point 26 miles from school and runs toward school at 6 miles per hour. Ryan starts from school 1.3 hours later and runs towards Sarah at 8 miles per hour. Let x be the number of hours Sarah has been running
Write an expression in terms of x for the distance Sarah has run
Write an expression in terms of x for Sarah's distance from the school
Write an expression in terms of x for the time Ryan has been running
Write an expression in terms of x for Ryan's distance from the school
Write and solve an equation to find when Sarah and Ryan meet
How far are they from the school when they meet uP
Sarah runs 6 x
sarah is 26 - 6 x from school
Ryan ran x -1.5 hours
ryan is 8 (x-1.5) from school
when they meet
Sarah runs 6 x
sarah is 26 - 6 x from school
Ryan ran x -1.5 hours
ryan is 8 (x-1.5) from school
when they meet
26 - 6 x = 8 (x-11.5)
can you take it from there?
26 - 6 x = 8 (x-1.5)
Thank you!!!
To solve this problem, let's break down the given information into equations.
1. Expression for the distance Sarah has run in terms of x:
Since Sarah runs at a constant speed of 6 miles per hour, the distance she runs can be expressed as "6x" miles.
2. Expression for Sarah's distance from the school in terms of x:
Sarah starts 26 miles away from the school and runs towards it, so her distance from the school can be expressed as "26 - 6x" miles. As she runs, the distance decreases.
3. Expression for the time Ryan has been running in terms of x:
Ryan starts running 1.3 hours after Sarah, so the time he has been running can be represented by "x - 1.3" hours.
4. Expression for Ryan's distance from the school in terms of x:
Ryan starts at the school and runs towards Sarah at a constant speed of 8 miles per hour. Therefore, his distance from the school can be expressed as "8(x - 1.3)" miles.
5. Equation to find when Sarah and Ryan meet:
To find when Sarah and Ryan meet, their distances from the school should be equal. Thus, we set Sarah's distance = Ryan's distance:
26 - 6x = 8(x - 1.3).
Let's solve this equation:
26 - 6x = 8x - 10.4
Adding 6x to both sides:
26 = 14x - 10.4
Adding 10.4 to both sides:
36.4 = 14x
Dividing by 14:
x = 2.6
Therefore, Sarah and Ryan meet after Sarah has been running for 2.6 hours.
6. Distance from the school when they meet:
To find this distance, substitute the value of x into one of the expressions we established earlier. Let's use Sarah's distance from the school expression:
Sarah's distance = 26 - 6x
Substituting x = 2.6:
Sarah's distance = 26 - 6(2.6)
Sarah's distance = 26 - 15.6
Sarah's distance = 10.4 miles
Hence, Sarah and Ryan are 10.4 miles away from the school when they meet.