# Cycled 70 miles at 18mph; 1st 10 miles at 16mph; what was speed during remaining 60 miles?

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#### Mark Wheatley

##### New member
Hi I have a question that I need some help with please. It is a real life situation and is about a cycle event I entered in to yesterday.
The cycle Ride was over 70 miles. I completed the whole 70 miles with an average speed of 18 miles an hour. However for the first 10 miles I rode with my wife and we were only averaging 16 miles an hour. So my question is how fast was my average over the 60 miles I was not riding with my wife. It must have been faster that 18 MPH as I had to make up for the 10 miles I did riding at 16 miles an hour ? Any help would be welcome - Many Thanks

#### Subhotosh Khan

##### Super Moderator
Staff member
To calculate the average speed (riding alone) - you need to know the time period that you rode alone.

First calculate the time you rode together. (distance)/(speed) = time → 10/16 hrs.

Also you need to calculate the time you have taken for the whole ride (together + alone). Again, (distance)/(speed) = time → 70/18 hrs.

So you rode alone (70/18 - 10/16 = ?) hrs.

So covered (70-10=) 60 miles in that time. From that calculate your average speed alone.

#### Denis

##### Senior Member
Using ye olde time = distance / speed:

Total time = 70/18 = 35/9 hr.
Time with wife: 10/16 = 5/8 hr.

Time w/o wife: 35/9 - 5/8 = 235/72 hr.

Is that enough?
Hope your wife forgives you for "dumping" her

#### Mark Wheatley

##### New member
To calculate the average speed (riding alone) - you need to know the time period that you rode alone.

First calculate the time you rode together. (distance)/(speed) = time → 10/16 hrs.

Also you need to calculate the time you have taken for the whole ride (together + alone). Again, (distance)/(speed) = time → 70/18 hrs.

So you rode alone (70/18 - 10/16 = ?) hrs.

So covered (70-10=) 60 miles in that time. From that calculate your average speed alone.
Hi thank you giving me some pointers

To follow up on your advice I rode the 10 miles with my wife in 51 minuets - It took me 4 hours 20 minuets to do the complete course of 70 miles how do these numbers fit in to your equations please

#### Mark Wheatley

##### New member
Using ye olde time = distance / speed:

Total time = 70/18 = 35/9 hr.
Time with wife: 10/16 = 5/8 hr.

Time w/o wife: 35/9 - 5/8 = 235/72 hr.

Is that enough?
Hope your wife forgives you for "dumping" her
Thank you for taking time to point me in the right direction
To follow up on your advice I rode the 10 miles with my wife in 51 minuets - It took me 4 hours 20 minuets to do the complete course of 70 miles how do these numbers fit in to your equations please
Your point about dumping my wife is well made - She was getting fed up of me trying to hurry her along, which is why she suggested I go ahead so I would annoy the other riders instead

#### Mark Wheatley

##### New member
Thank you for taking time to point me in the right direction
To follow up on your advice I rode the 10 miles with my wife in 51 minuets - It took me 4 hours 20 minuets to do the complete course of 70 miles how do these numbers fit in to your equations please
Your point about dumping my wife is well made - She was getting fed up of me trying to hurry her along, which is why she suggested I go ahead so I would annoy the other riders instead
Hi Sorry got the total time wrong it wasn't 4 hours 20 minuets it was in fact 3 hours 55 Minutes so I think I was averaging 19.46 miles per hour doing the 60 miles on my own ?

#### Mark Wheatley

##### New member
Hi thank you giving me some pointers

To follow up on your advice I rode the 10 miles with my wife in 51 minuets - It took me 4 hours 20 minuets to do the complete course of 70 miles how do these numbers fit in to your equations please
Hi thank you giving me some pointers

To follow up on your advice I rode the 10 miles with my wife in 51 minuets - It took me 4 hours 20 minuets to do the complete course of 70 miles how do these numbers fit in to your equations please
Hi Sorry got the total time wrong it wasn't 4 hours 20 minuets it was in fact 3 hours 55 Minutes so I think I was averaging 19.46 miles per hour doing the 60 miles on my own ?

#### Denis

##### Senior Member
Close...I make it 19.56

3h 55m = 235m
Time = 235 - 51 = 184 minutes = 184/60 hours
60 / (184/60) = 19.5652.......

#### Mark Wheatley

##### New member
Denis - Many thanks for your help I will sleep better now I have got that sorted in my head

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