Speed questions worded incorrectly?

[MathsFormula]

QUESTION A car completes a journey in 10 mins. For the first half of the distance the speed was 60 km/h and for the second half the speed was 40 km/h. How far is the journey?

Answer in book is 8 km. I can't get that answer.

I'll show you my efforts but I think I'm wasting time if the question is wrong. How can the first half of the distance be the same as the second half if the speeds are different?

Before I carry on attempting I need to ensure that I've got 10 mins correctly converted to hours.
10 mins = 10/60 hours = 0.16 hours?

Please advise. Thank you

 

[MathsFormula]

Almost got it Denis. I've decided that the question is just worded poorly.

The question says "for the first half of the distance" so I thought they meant the distance of the two parts of the journey were equal i.e both cars travelled a distance X km.

But what they actually mean is "the time travelled at both speeds was the same".

Therefore at 60 km/h the car travelled for 5 mins and at 40 km/h the car travelled for 5 mins.

5 mins = 5/60 = 0.083

Now 60 km/h means 60 = km/h

60 = d₁/t

60 = d₁/0.083

d₁=4.98 km


Same method for the travel at 40 km/h gives d₂=3.32 km

So total journey = 8.3 km ALMOST CORRECT.

Answer in book is exactly 8km


If I take 5 mins as 0.08 then the answer is exactly 8km.

Have I gone wrong somewhere? The book doesn't ask for the answer to be to the nearest km.

Please advise further. Thanks

 

[Ishuda]

Almost got it Denis. I've decided that the question is just worded poorly.

The question says "for the first half of the distance" so I thought they meant the distance of the two parts of the journey were equal i.e both cars travelled a distance X km.

But what they actually mean is "the time travelled at both speeds was the same".

Therefore at 60 km/h the car travelled for 5 mins and at 40 km/h the car travelled for 5 mins.

5 mins = 5/60 = 0.083

Now 60 km/h means 60 = km/h

60 = d₁/t

60 = d₁/0.083

d₁=4.98 km


Same method for the travel at 40 km/h gives d₂=3.32 km

So total journey = 8.3 km ALMOST CORRECT.

Answer in book is exactly 8km


If I take 5 mins as 0.08 then the answer is exactly 8km.

Have I gone wrong somewhere? The book doesn't ask for the answer to be to the nearest km.

Please advise further. Thanks

The distance traveled is the same, but since you are going faster one time than the other, the times are not the same. So
60 t₁ = d₁ = d₂ = 40 t₂
and the total time they traveled was 1/6 hr
t₁ + t₂ = 1/6

 

[Deleted member 4993]

QUESTION A car completes a journey in 10 mins. For the first half of the distance the speed was 60 km/h and for the second half the speed was 40 km/h. How far is the journey?

Answer in book is 8 km. I can't get that answer.

I'll show you my efforts but I think I'm wasting time if the question is wrong. How can the first half of the distance be the same as the second half if the speeds are different?

Before I carry on attempting I need to ensure that I've got 10 mins correctly converted to hours.
10 mins = 10/60 hours = 0.16 hours? (leave it as 1/6 - it is not a good idea to truncate here. However, if you had to truncate it would be 0.17 or 0.167 or 0.1667, etc.)

Please advise. Thank you

Another way:

Let the total distance travelled = 2*d miles

Time for first half of the distance (d) = t₁ = d/60 hours

Time for second half of the distance (d) = t₂ = d/40 hours

so

d/60 + d/40 = 1/6 ....... solve for d → 2*d

 

[Dale10101]

And

QUESTION A car completes a journey in 10 mins. For the first half of the distance the speed was 60 km/h and for the second half the speed was 40 km/h. How far is the journey?

Answer in book is 8 km. I can't get that answer.

I'll show you my efforts but I think I'm wasting time if the question is wrong. How can the first half of the distance be the same as the second half if the speeds are different?

Before I carry on attempting I need to ensure that I've got 10 mins correctly converted to hours.
10 mins = 10/60 hours = 0.16 hours?

Please advise. Thank you

The trip is a distance D.

The first half of the distance, D/2 is traveled in time t at 60 km/hr. So ...

eq1: D/2 = (t)(60 km/hr)

The second half of the distance, also D/2 is traveled in the remaining time (1/6 hr -t) at 40 km/hr. So ...

eq2: D/2 = (1/6 hr - t)(40 km/hr), equating the RHS of eq1 and eq2 gives:

eq3: t(60) = (1/6 - t)(40), solve for t and insert the result in eq1 or eq2 and solve for D, result 8 km.

also, 1hr/60 min = t hr/10 min, t = (1/6) hr