Question

Jorden drives to the store at 30 miles per hour. on her way home she averages only 20 miles per hour. if the total driving time takes half an hour, how far does she live from the store?fill out the distance column. c = d =

Answer 1

By using the relationship between speed, distance, and time, we find out that Jorden lives 4 miles away from the store. We derived the time spent on each leg of the trip and used them to calculate the distance.

Step-by-step explanation:

To solve the problem, we'll define distance (d), speed (s), and time (t). Remember, the formula for speed is s = d/t, and rearranging for distance gives us d = s × t.

Let's define t1 as the time taken to travel to the store and t2 as the return time. Given that the total time is 0.5 hours and knowing that the speeds are 30 mph to the store and 20 mph back, we can write two equations:

• For the trip to the store: d = 30 × t1
• For the trip home: d = 20 × t2

Since the total time is 0.5 hours, we have t1 + t2 = 0.5. Using these equations, we can solve for d by expressing one of the times in terms of the other and then substituting back into one of the distance equations.

Let's express t1 in terms of t2:
t1 = 0.5 - t2.
Substitute t1 into the first distance equation: d = 30 × (0.5 - t2). Set this equal to the second distance equation d = 20 × t2. Solve the resulting equation for t2 and finally, calculate d.

After solving, we find that t2 = 0.2 hours (12 minutes) and t1 = 0.3 hours (18 minutes). Substituting either t2 into d = 20 × t2 or t1 into d = 30 × t1 gives us d = 4 miles. Therefore, Jorden lives 4 miles away from the store.