Hamza lives 35 miles from his office. On the way to work, he drove at his normal speed, but on the way home, traffic caused his driving speed to decrease by 5 miles per hour. The trip home took 2 hours. What was Hamza’s speed on his way to work?
Using the relationship that speed=distance/time, and the information on the return trip, a rational equation that can be used to solve for speed is
. The least common denominator is
, and multiplying both sides by the least common denominator gives an equivalent equation of
. Write the solution to this equation as a decimal:
miles per minute.
The rational equation that can be used to solve for speed is:
35/(x - 5) = 2
In this equation, x represents Hamza's speed on his way to work.
Multiplying both sides of the equation by the least common denominator, which is (x - 5), gives:
35 = 2(x - 5)
35 = 2x - 10
Adding 10 to both sides of the equation gives:
45 = 2x
Dividing both sides of the equation by 2 gives:
x = 22.5
So, Hamza's speed on his way to work was 22.5 miles per hour.
To convert this to miles per minute, we divide by 60 (since there are 60 minutes in an hour):
22.5 miles per hour = 22.5/60 miles per minute = 0.375 miles per minute.
To find Hamza's speed on his way to work, we first need to calculate the time it took for him to drive home.
Given:
Distance from home to office = 35 miles
Time taken to drive home = 2 hours
We know that speed = distance / time. Rearranging the equation to solve for time, we have:
Time = distance / speed
Using the information from the problem, we can write the equation:
2 = 35 / (speed - 5)
Next, we can solve this equation for speed.
To get rid of the fraction, we can multiply both sides of the equation by (speed - 5):
2(speed - 5) = 35
Expanding the left side:
2speed - 10 = 35
Add 10 to both sides:
2speed = 45
Divide both sides by 2:
speed = 45 / 2
Calculating the result:
speed = 22.5 miles per hour
So, Hamza's speed on his way to work was 22.5 miles per hour.
To find Hamza's speed on his way to work, we can use the given information and the equation speed = distance/time.
Let's denote Hamza's speed on his way to work as "x" miles per hour.
On the way to work, the distance traveled is 35 miles, and we don't have information about the time taken.
On the way back home, Hamza's speed was reduced by 5 miles per hour, resulting in a speed of (x - 5) miles per hour. The time taken for the return trip is given as 2 hours.
Using the equation speed = distance/time, we can set up the equation as follows:
(x - 5) = 35 / 2
Simplifying the equation further, we have:
x - 5 = 17.5
To solve for x, we can isolate it by adding 5 to both sides of the equation:
x = 17.5 + 5
x = 22.5
Therefore, Hamza's speed on his way to work was 22.5 miles per hour.