danny drove halfway from town p to town q at average speed of 60 km/h. he wants to average 80 km/h for the entire journey. What will his average speed be for the second part of his journey?
speed=distance/time
60=d/2time1
but d=60*time1+V*time2
and
80=d/(time1+time2)
or
time1+time2=d/80 then
d/120+time2=d/80
time2=d/80-d/120=d/120 (3/2-1)
time2=d/240
so velocity2ndpart=(d/2)/time2
= d/2(d/240)=120km/hr
check:
time1=d/(2*60)=d/120
time2=d/(2*120)=d/240
80=d/(time1+time2)=d/(3d/240)=80
To find out Danny's average speed for the second part of his journey, we'll need to gather some information.
Let's say the total distance from town P to town Q is D km. Since Danny drove halfway, he covered (1/2)D km.
Now, let's calculate the time he took for the first part of the journey:
Time = Distance / Speed
Time = (1/2)D / 60 km/h
Time = (1/2D) * (1/60) hours
Next, we need to calculate the time he has remaining for the second part of the journey. Since he wants to average 80 km/h for the entire journey, we can use the remaining distance (1/2)D and the desired average speed of 80 km/h.
Time = Distance / Speed
Time = (1/2)D / 80 km/h
Time = (1/2D) * (1/80) hours
To find the average speed for the second part of the journey, we'll divide the remaining distance by the remaining time:
Average Speed = Distance / Time
Average Speed = (1/2)D / [(1/2D) * (1/80)]
Average Speed = (1/2)D * [(80/(1/2D))]
Average Speed = 2 * 80
Average Speed = 160 km/h
Therefore, Danny's average speed for the second part of his journey will be 160 km/h.