Question

After driving to a riverfront parking lot, Bob plans to run south along the river, turn around and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

Answer 1

Hint: First find the distance travelled by Bob at this speed for a given time. Now add the already travelled distance to this distance. This sum Gives you the whole distance travelled in the round trip. Now if we divide it by 2 then we get distance travelled in the south. Already he travelled some of this south distance. So, by subtracting the travelled distance from this total south distance you get the extra distance, which is the required result.

Complete step-by-step solution -
Distance travelled in the south direction, given in the question, as: 3.25 miles.
The constant rate at which Bob drives is given by (value): 8 minutes per mile.
The time he decided to travel more is given as” 50 minutes.
By basic of measurements, we know the formulas:
$Rate=\dfrac{time\,\,taken}{distance\,\,travelled}$
Now by substituting the values of rate, time, we get:
$8=\dfrac{50}{distance}$
By multiplying with distance on both sides, we get it as:
\[8\times distance=50\]
By dividing with 8 on both sides, we get it as:
$distance=\dfrac{50}{8}$
By simplifying the right-hand side, we get value of d as:
Distance= 6. 25 miles
The distance travelled in the next 50 minutes is 6.25 miles.
He already travelled a distance of 3.25 miles. This distance and 6.25 together gives a distance of round trip.
By above statement, we can find value of round trip:
Round trip = (6.25+3.25) miles.
By simplifying above equation, we get value as:
Round trip = 9.5 miles
So, by this we say the whole trip of Bob is 9.5 miles. It includes distance travelled both directions south and north. It is given that he must return to the parking lot. So, distance travelled south must be equal to distance travelled north round trip= south + north.
By substituting distance north = distance south, we get it as:
2(south)=round trip
He already travelled 3.25 miles, so let the entrance be x miles. From question we get south = 3.25+x. by substituting this
2(3.25+x)= round trip
By substituting round trip and dividing with 2, we get it as:
3.25+x=4.75
By substituting with 3.25 on both sides, we get it as:
x= 4.75-3.25
By simplifying above equation, we get the value of x as:
x=1.5 miles farther south
Therefore, the extra distance he needs to cover to get return in 50 miles is 1.5 miles farther south.

Note: As the steps are more students confuse where to substitute what. So, do each and every thing step by step carefully. While calculating distance in 50 min. Every student generally thinks it is speed and distance/time but if you look closely at units it is time/distance.