1) An aircraft flying at 500 km/h completes a journey in 8.4 h. How long would the journey take if it flew at a speed of 420 km/h?
2) Jackie can drive to work in 18 mins if he travels at an average speed of 35 m.p.h. How long will the journey take if she drives at an average speed of 45 m.p.h.?
Thnx
To solve these problems, you can use the formula:
Time = Distance / Speed
Let's go step by step for each problem:
1) An aircraft flying at 500 km/h completes a journey in 8.4 h. How long would the journey take if it flew at a speed of 420 km/h?
Step 1: Let's assume the distance of the journey is D km.
Step 2: We can use the formula to write the equation for the given scenario:
Time (T1) = Distance (D) / Speed (500 km/h)
T1 = D / 500
Step 3: We can also write the equation for the new scenario:
Time (T2) = Distance (D) / Speed (420 km/h)
T2 = D / 420
Step 4: Since the time taken in both scenarios is the same (8.4 hours), we can equate T1 and T2:
T1 = T2
D / 500 = D / 420
Step 5: Now let's solve for D:
D / 500 = D / 420
420D = 500D (Cross-multiplying)
500D - 420D = 0
80D = 0
D = 0
Step 6: From the equation, we can see that the distance is 0 km. Therefore, it is not possible to determine how long the journey would take if the aircraft traveled at 420 km/h.
2) Jackie can drive to work in 18 mins if he travels at an average speed of 35 m.p.h. How long will the journey take if she drives at an average speed of 45 m.p.h.?
Step 1: Let's convert the time into hours:
Time (T1) = 18 mins = 18/60 = 0.3 hours
Step 2: We can use the formula to write the equation for the given scenario:
Time (T1) = Distance (D) / Speed (35 m.p.h.)
0.3 = D / 35
Step 3: Now we can solve for D:
0.3 = D / 35
D = 0.3 * 35
D = 10.5 miles
Step 4: Now we can find the time it will take if Jackie drives at an average speed of 45 m.p.h. by using the same formula:
Time (T2) = Distance (D) / Speed (45 m.p.h.)
T2 = 10.5 / 45
T2 = 0.23 hours
Step 5: Let's convert the time back into minutes:
T2 = 0.23 * 60 = 13.8 minutes
So, the journey will take approximately 13.8 minutes if Jackie drives at an average speed of 45 m.p.h.
To solve both of these questions, we can use the formula:
Time = Distance / Speed
1) For the first question, we are given the speed of the aircraft (500 km/h) and the time it takes to complete the journey (8.4 hours). We need to find out how long the journey would take if the aircraft flew at a speed of 420 km/h.
Let's define the time taken at the speed of 420 km/h as 't'.
We know that the distance covered by the aircraft is the same in both cases, regardless of the speed. Therefore, we can set up the following equation:
Distance / 500 km/h = Distance / 420 km/h
By cross-multiplying, we get:
Distance * 420 km/h = Distance * 500 km/h
Simplifying the equation, we can cancel out the common 'Distance' term:
420 km/h = 500 km/h
We can solve for 't' by cross-multiplying once again:
t = 8.4 hours * 420 km/h / 500 km/h
t = 7.056 hours
Therefore, the journey would take 7.056 hours, or approximately 7 hours and 3 minutes, if the aircraft flew at a speed of 420 km/h.
2) For the second question, we are given a different scenario. Jackie can drive to work in 18 minutes with an average speed of 35 mph. We need to find out how long the journey will take if she drives at an average speed of 45 mph.
Let's define the time taken at the speed of 45 mph as 't'.
We know that the distance covered by Jackie is the same in both cases, regardless of the speed. Therefore, we can set up the following equation:
Distance / 35 mph = Distance / 45 mph
Again, by cross-multiplying, we get:
Distance * 45 mph = Distance * 35 mph
Simplifying the equation, we can cancel out the common 'Distance' term:
45 mph = 35 mph
Once again, cross-multiplying, we can solve for 't':
t = 18 minutes * 45 mph / 35 mph
t = 23.143 minutes
Therefore, the journey would take approximately 23.143 minutes, or approximately 23 minutes and 9 seconds, if Jackie drives at an average speed of 45 mph.
#1
Recall that rate is distance traveled over time.
r = d/t
or solving for distance,
d = rt
We can therefore write the proportion as
(rate1)*(time1) = (rate2)*(time2)
(500)*(8.4) = (420)*(time2)
Now solve for time2. Units in hours.
#2
Same what you'll do here in #2.
(rate1)*(time1) = (rate2)*(time2)
(35)*(18) = (45)*(time2)
Now solve for time2. Units in minutes.
Hope this helps~ `u`