If a car travels for a distance of 16 km at an average speed of 50 km/h and then for a distance of 52 km at an average speed of 80 km/h, what is the total time for the journey in minutes, to the nearest minute?
(16/50+52/80)*60min
=(0.32+0.65)*60 min
=0.97*60 min
=58.2 min
=58 min. (to the nearest minute)
To find the total time for the journey, we can use the formula:
Time = Distance / Speed
First, let's calculate the time for the first part of the journey. The car travels a distance of 16 km at an average speed of 50 km/h. Plugging these values into the formula:
Time = 16 km / 50 km/h
To simplify this calculation, let's convert the units to be consistent. We'll convert 50 km/h to km/minute by dividing it by 60:
Time = 16 km / (50 km/h * (1 h / 60 min))
Simplifying further:
Time = 16 km / (50 km/h * (1/60 min/h))
Time = 16 km / (50 km/h * 1/60 min/h)
Cancelling the units:
Time = (16 km * 60 min) / (50 km * 1)
Time = (960 km·min) / 50 km
Now, let's calculate the time for the second part of the journey. The car travels a distance of 52 km at an average speed of 80 km/h. Applying the same steps as above:
Time = 52 km / 80 km/h
Time = (52 km * 60 min) / (80 km * 1)
Time = (3120 km·min) / 80 km
Finally, to find the total time for the entire journey, we can add the two times together:
Total Time = (960 km·min) / 50 km + (3120 km·min) / 80 km
To combine these fractions, we need a common denominator. The least common multiple of 50 and 80 is 400. Let's rewrite the fractions using this denominator:
Total Time = (960 km·min * 8) / (50 km * 8) + (3120 km·min * 5) / (80 km * 5)
Now that the denominators are the same, we can add the numerators:
Total Time = (7680 km·min + 15600 km·min) / (400 km)
Total Time = 23280 km·min / 400 km
Finally, let's convert the total time from hours to minutes by multiplying by 60:
Total Time = (23280 km·min / 400) min
Total Time = 58.2 min
Rounding to the nearest minute, the total time for the journey is approximately 58 minutes.