Question

Can someone plz help me with these 2 problems

1.A tourist was planning a trip by car for travelling at some constant speed for 2.5 hours. However, he found that if he increases the speed by 20 km/h he can cover the same distance in 30 minutes less time than it was planned. What was the planned speed of the tourist, in km/h?

2.A jet ski with average speed of 60 mph left a pier by the river upstream. Fifteen minutes after its motor broke, and it began drifting downstream for 3 hours and 45 minutes until reached another pier, which was 2 miles away down the river from the original pier. What is the rate of the current, in mph?

Answer 1

Explanation:

1. let planned speed be x

distance planned=2.5x

new speed=x+20

new time=2.5-30/60 cuz' theres 60min in 1 hr

=2.5-0.5=2

so distance planned=2(x+20)

2(x+20)=2.5x

2x+40=2.5x

0.5x=40

x=80km/h

2. let rate of current be x

ski's total time in water=3h45m+15m=4h

total distance by current drift=4x

ski motor'd upstream at 60mph for 15m i.e. 0.25h

distance motor'd is -ve as it is "upstream"

=-60(0.25)=-15mile

combining motor'd n drift distances, 4x-15=2

4x=17

x=4.25mph

Answer 2

1. r = 80 km/h

2. The current is flowing at 4.25 mph

Explanation:

1. Distance = rate * time

Distance = r * 2.5

If he increase the rate by 20 = (r+20),

the time is 30 minute = .5 hours less =(t-.5)

The time was 2.5 hours = (2.5-.5) = 2 hours

Distance = (r+20) 2 hours

The distance is the same so we set the equations equal

2.5r = 2 * (r+20)

Distribute

2.5r = 2r +40

Subtract 2r from each side

2.5r -2r = 2r-2r +40

.5r = 40

Divide by .5

.5r /.5 = 40/.5

r = 80 km/h

2. Distance = rate * time

rate = 60-r time = 15 minutes/60 minute = .25 hours

Distance = (60-r) * .25

where r is the rate of the current

While drifting it is affected by the current only

Now time = 3 hours 45 minutes = 3 .75 hours

Distance is the the distance it traveled while jetskiing plus 2 miles

Distance +2 = r* (3.75)

Substituting for distance

(60-r) * .25 +2 = 3.75 r

Distribute

15 -.25r +2 = 3.75r

Combine like terms

17 -.25r = 3.75r

Add .25r to each side

17-.25r +.25r = 3.75r +.25r

17 = 4r

Divide by 4

17/4 = 4r/4

4.25 =r

The current is flowing at 4.25 mph