The school is how many ​mile(s) from their house.

Question

A brother and a​ sister, Sofia and​ Daniel, jog to school daily.​ Sofia, who is​ older, jogs at

10 miles per hour. Daniel jogs at 6 miles per hour. When Sofia reaches the​ school, Daniel is

3/4 mile away. How far is the school from their​ house?

Answer 1

Distance = rate times time

D = R•T

Let "x" be the distance to school.

Let's say they both left at the same time:

The distance Sofia went (all the way to school) would be x and we can say x = her rate times her time (we'll say her time is T) so x = 10T

The distance Daniel went was (x - 3/4) and we can say (x - 3/4) = his rate times Sofia's time T, so (x - 3/4) = 6T

We can plug in 10T for "x" in the second equation giving us:

10T - 3/4 = 6T

4T = 3/4

T = 3/16 (of an hour)

Plugging that into the equation x = 10T we get x = 10(3/16) = 30/16 miles = 15/8 miles or 1.875 miles.

Checking this: If Sofia ran 1.875 miles at 10m/hr it would take her 1.875/10 = 0.1875 hrs. During that time, Daniel would have traveled 6(0.1875) = 1.125 miles and he would still have 1.875 - 1.125 or 0.75 miles to go. So it checks out. Yay!!

Answer 2

Given the information provided, we can start by trying to figure out the appropriate equation that describes the situation. We will have to pay attention to the units as we go along to make sure that everything works out. Let's start with saying that 10 mi/hr * some variable = 6 mi/hr * that same variable + 3/4 mi. This describes how Sofia's and Daniel's positions are related. Now this "variable" needs to make sense from a units stand point. Our units need to end up being miles because of our 3/4 miles term. So: miles/hour times hours should give us just miles. Our "some variable" is time. Let's rewrite the equation: 10 mi/hr * t hr = 6 mi/hr * t hr + 3/4 mi. We can then solve this equation by combining the "t" terms on one side of the equation and have everything else on the other side of the equation, leaving: 10*t - 6*t = 3/4 (dropping the units for a moment). This simplifies to 4 mi/hr * t hr = 3/4 mi. We can them solve and find that t = 3/16 hours. Now, we aren't quite done yet because we have to find the distance to their school. We can simply plug our value for "t" back into our original equation to find that 10 mi/hr * 3/16 hr = 1.875 miles.